• /

Analysis and Optimization of Preliminary Aircraft

Configurations in Relationship to Emerging Agility Metrics

GRANTOR - NASA AMES RESEARCH CENTER

GRANTEE - CAL POLY STATE UNIVERSITY

GRANT NUMBER NAG 2 743

9/15/91-9/14/93

Principal Investigator

Dr. Doral 1L Sandlin

Student Investigator

Brent Alan Bauer

December 1993

(NASA-CR-|9_Z28) ANALYSIS ANO

OPTIMIZATION OF PRELIMINARYAIRCRAFT CONFIGURATIONS IN

RELATIONSHIP TO EMERGING AGILITY

METRICS Final Report, 15 Sep. 1991

- 14 Sep. 1993 (California

polytechnic State univ.) 133 p

N94-26235

uncla$

G3/05 0209455

https://ntrs.nasa.gov/search.jsp?R=19940021732 2020-03-15T14:39:23+00:00Z

ABSTRACT

Analysis and Optimization of Preliminary Aircraft

Configurations in Relationship to Emerging Agility Metrics

by

Brent Bauer

December 1993

This paper discusses the development of a FORTRAN computer

code to perform agility analysis on aircraft configurations. This

code is to be part of the NASA-Ames ACSYNT (AirCraft SYNThesis)

design code. This paper begins with a discussion of contemporary

agility research in the aircraft industry and a survey of a few

agility metrics. The methodology, techniques and models developed

for the code are then presented. Finally, example trade studies using/

the agility module along with ACSYNT are illustrated. These trade

' studies were conducted using a Northrop F-20 Tigershark aircraft

model. The studies show that the agility module is effective in

alalyzing the influence of common parameters such as thrust-to-

weight ratio and wing loading on agility criteria. The module can

compare the agility potential between different configurations. In

addition one study illustrates the module's ability to optimize a

configuration's agility performance.

P_N_ PAGE Bt.ANK NOT FFLMED

TABLE OF CONTENTS

Page

LIST OF TABLES ......................................................................................................... vii

LIST OF FIGURES ...................................................................................................... v i i i

LIST OF SYMBOLS_°_-°°IHe--_1II_-_j°---_I--°----j-_-_--_H-_-°----_-_--_°---_--_---_----_--_-_-_---_-------o X i

CHAPTER

°

2.

°

°

INTRODUCTION ............................................................................................. 1

DISCUSSION ON AGILITY METRICS ....................................................... 5

The Doghouse Plot and Definition of Corner Speed .............. 5Survey of Agility Metrics ................................................................ 7

Combat Cycle Time ................................................................. 7

Pointing Margin ........................................................................ 8

Torsional agility ................................................................... 10

Axial agility ........................................................................... 10

Dynamic Speed Turn ............................................................ 10

Agility Metrics in Relation to Project Scope and

Code Architecture ............................................................................ 12

GENERAL METHODOLOGY ........................................................................ 14

Constant Altitude ............................................................................. 15

Breakup of Maneuvers Into Segments ...................................... 16

Tracked Variables ............................................................................ 19

FLIGHT DYNAMICS ................................................................................... 22

Coordinate Systems ........................................................................ 22

Development of Free-Body Diagrams and Equationsof Motion for Functional Maneuver Segments ...................... 25Equations of Motion for Transient Maneuver

Segments .............................................................................................. 30

Roll Segments ........................................................................ 31

Pitch Segments ..................................................................... 33

5. ENGINE THRUST TRANSIENT DEVELOPMENT .................................. 41

P_'_; _A__,_ _L.ArVK NOT FFLMED

V

° CODE OPTIONS AND FEATURES ........................................................... 46

Angle of Attack Limiting .............................................................. 46

Definition of Turning Speed ......................................................... 47

Throttle Control and Turning Speed Capture ........................ 49

Thrust Vectoring .............................................................................. 52Air brake .............................................................................................. 53

External Stores Release and Weight/Moment ofInertia Control ................................................................................... 54

o CODE VERIFICATION ............................................................................... 56

Continuity of Tracked Variables ............................................... 57

Agreement With ACSYNT's Combat Analysis ........................ 57

o EXAMPLE STUDIES ................................................................................... 62

Effect of Thrust Loading on Combat Cycle Time ................ 63

Effect of Wing Loading on Combat Cycle Time .................... 73Use of Combat Cycle Time as a Constraint In

Aircraft Optimization .................................................................... 82

9. CONCLUSIONS AND RECOMMENDATIONS ......................................... 87

LIST OF REFERENCES ................................................................................................ 90

APPENDIX A ................................................................................................................. 94

Description of Baseline Aircraft for Verification and

Example Studies ............................................................................................ 94

APPENDIX B.................................................................................................................. 96User's Manual ................................................................................................ 96

vi

TABLES

Table Page

3.1 Variables Tracked Over Time by the Agility Module ...........21

5.1 Throttle Response Time Histories Obtained fromContemporary Fighter Engine for Use in the AgilityModule ..................................................................................................41

7.1 Correlation of Agility Module Parameters withParameters Calculated in COMBAT Phases of theTrajectory Module at Mach 0.73 ...............................................59

7.2 Correlation of Agility Module Parameters withParameters Calculated in COMBAT Phases of theTrajectory Module at Mach 0.68 ...............................................60

7.3 Correlation of Agility Module Parameters withParameters Calculated in COMBAT Phases of theTrajectory Module at Mach 0.53 ...............................................61

8.1 Design Space Boundaries and Final Results forCombat Cycle Time Optimization ............................................85

vii

Figure

2.1

2.2

2.3

FIGURES

Page

Illustration of the Doghouse Plot ................................................6

Combat Cycle Time Maneuver Circuit ......................................... 8

Pointing Margin Agility Metric ...................................................... 9

2.4a Plot of Turn Rate Versus Bleed Rate for theDynamic Speed Turn Metric .....................................................11

2.4b Plot of Level Acceleration Versus Velocity for theDynamic Speed Turn Metric ..................................................... 12

3.1 Downward Vertical Acceleration Due to

Unbalanced Weight Vector at a Bank Angle ...................... 16

3.2 Breakup of Metric Maneuvers into Maneuver

Segments ......................................................................................... 18

3.3 Illustration of the Agility Maneuver SegmentCategories ....................................................................................... 19

4.1 Orientation of the Inertial Coordinate Frame and

the Translating Coordinate Frame ........................................ 24

4.2 Orientation of the Rotating Coordinate Frame With

Respect to the Translating Coordinate Frame ................ 25

4.3 Free Body Diagram for the Axial Acceleration

Component ....................................................................................... 29

4.4 Free Body Diagram for the Normal Acceleration

Component ....................................................................................... 30

4.5 Illustration of a Typical Roll Maneuver ................................. 33

4.6 Typical Pitch Response to a Step ElevatorDeflection ........................................................................................ 38

viii

4.7 Comparison of Pitch Response Due to a Single andMultiple Elevator Deflection ................................................... 39

4.8 Load Factor Pitch Response With and WithoutDynamic Term ................................................................................40

5.1a Throttle Transient Response from Flight Idle toMaximum Afterburner ................................................................42

5.1b Throttle Transient Response from Flight Idle toMaximum Dry Thrust ...................................................................43

5.1c Throttle Transient Response from Maximum DryThrust to Maximum Afterburner ............................................ 43

5.1d Throttle Transient Response from MaximumAfterburner to Maximum Dry Thrust ...................................44

5.1e Throttle Transient Response from Maximum DryThrust to Flight Idle ...................................................................44

5.1f Throttle Transient Response from MaximumAfterburner to Flight Idle ........................................................45

5.2 Throttle Transient Response Starting from PartialDry Throttle up to Maximum Afterburner .......................... 45

6.1 Typical Lift Curves Generated By ACSYNT ............................4 7

6.2 Variation of Turning Speed With Turning LoadFactor ................................................................................................49

6.3 Illustration of Throttle Control Logic as AircraftPasses Through Turning Speed ...............................................50

6.4 Illustration of Throttle Control Logic When theMLEAD Parameter is Employed ...............................................52

8.1 Northrop F-20 Tigershark Three View .................................... 63

Jx

8.2 Combat Cycle Time Variation for Different Thrust

Loadings ........................................................................................... 68

8.3 Mach Number Time Histories for Different Thrust

Loadings ........................................................................................... 69

8.4 Turn Rate Time Histories for Different Thrust

Loadings ........................................................................................... 70

8.5 Horizontal Plane Turn Diagrams for Different

Thrust Loadings ............................................................................ 71

8.6 Load Factor Time Histories for Different Thrust

Loadings ........................................................................................... 72

8.7 Combat Cycle Time Variation for Different WingLoadings ........................................................................................... 77

8.8 Mach Number Time Histories for Different WingLoadings ........................................................................................... 78

8.9 Turn Rate Time Histories for Different WingLoadings ........................................................................................... 79

8.10 Horizontal Plane Turn Diagrams for Different WingLoadings ........................................................................................... 80

8.11 Load Factor Time Histories for Different WingLoadings ........................................................................................... 81

8.12 Optimization Path for Minimization of Aircraft

Takeoff Weight .............................................................................. 86

ctF

ac._nt

a z

CL

CD

CLa

CLac

CLah

CMa

CMa

C Mq

D aero

DYa1_l

SYMBOLS

Acceleration normal to flight path due to aerodynamic andthrust forces

Centripetal acceleration (reaction)

Acceleration along flight path direction

Aircraft lift coefficient

Aircraft drag coefficient

Aircraft lift slope

Canard lift slope

Horizontal tail lift slope

Aircraft pitching moment coefficient due to angle of

attack

Aircraft pitching moment coefficient due to angle of

attack rate (-_-_-)

Aircraft pitching moment coefficient due to pitch rate

Parasite plus induced drag force (D_,,o=qSCD)

Ram drag force (Ts-T.)

Upwash gradient at canard

Downwash gradient at horizontal tail

xi

g

L.

Liy A

M

M a

M6t

Mq

M_

n dgn

P

Ps

R

gravitational acceleration

Aircraft lift force (L=qSCL), or aircraft rolling moment

Roll damping derivative I'll

Aileron effectiveness derivative

Mach number

Aircraft pitching moment derivative due to angle of attack

Aircraft pitching moment derivative due to angle of attack

rate -_-

Aircraft pitching moment derivative due to pitch rate

Aircraft pitching moment derivative due to control

surface deflection- elevator/canardvator _

Load factor

Transient load factor term due to pitch rate

Roll rate

Specific excess power

Steady state roll rate

Turn radius

xii

U 1

V

V C

W

X

Xac_

Xac k

Xcg

¥

Z a

Z_

&

Time

Gross thrust

Net thrust

Steady state forward airspeed

Instantaneous forward airspeed

Canard volume coefficient or aircraft corner speed

Horizontal tail volume coefficient

Acceleration along flight path, equivalent to ax

Aircraft weight

Downrange distance, used to track movement of aircraft

Longitudinal location of canard aerodynamic center onaircraft

Longitudinal location of horizontal tail aerodynamiccenter on aircraft

Longitudinal location of center of gravity on aircraft

Crossrange distance, used to track movement of aircraft

Normal force derivative due to angle of attack

Normal force derivative due to control surface deflection-

e levator/canardvator

Angle of attack

Pitch control surface deflection

xiii

Z_

1"//I

O

;L

Aileron deflection

Incremental difference

Dynamic pressure ratio at canard location

Dynamic pressure ratio at horizontal tail location

Aircraft pitch angle

Thrust vector angle

Bank angle

Heading angle

Turn Rate

xiv

CHAPTER 1

INTRODUCTION

Much of present fighter performance research centers on

agility. Projects such as NASA's High Angle of Attack Research

Vehicle (HARV)I and Rockwell/MBB's X-31 agility research

platform2,3 represent the flight test efforts at agility research. In

addition, in the past five to ten years, increased interest from

industry and NASA have created a host of analysis methods and

agility philosophies.4,s,s,7 Several companies have developed their

own measures of merit, or metrics, that they believe best measure

an aircraft's agility. However, the industry as a whole has not yet

adopted a solid definition of agility nor accepted any of the analysis

methods or metrics as superior.

Some of the agility definitions used by industry are:

The ability to change aircraft attitude and

flight path with quickness and precisionAir Force Flight Test Center8

Agility is directly proportional to the inverse

of the time to transition from one maneuverto another

Pierre Sprey7

Agility is the ability to rapidly change boththe magnitude and direction of the aircraftvelocity vector

Northrop7

2

Agility is an attribute of a fighter aircraftthat measures the ability of the entireweapon system to minimize the time delaysbetween target acquisition and targetdestruction

Eidetics7

While all of these definitions appeal to the intuitive sense of

what agility should address, they each place emphasis on different

facets of the concept of agility. These different approaches have

thus provided different tools and parameters to analyze the agility

potential of an aircraft configuration. It is these various facets and

their respective tools and parameters that have produced the myriad

of agility metrics. Chapter Two discusses in detail some of these

metrics.

The importance of agility is to provide a combat advantage

over other aircraft. Combat advantage can be provided by superior

training, better weapons, as well as many other sources. However,

improvement in an airframe's performance has always been a key

element in providing combat advantage. Historically, this has been

created through improvements in energy maneuverability; the ability

to generate high turn rates and high speeds and accelerations. The

energy maneuverability envelope has been continuously expanded

from the days of World War I until today. However, the last

generation of fighters reached an envelope boundary. This boundary

is the physiological limit of the pilot. Contemporary aircraft have

surpassed the g tolerance of humans and this has placed a limit on

combat advantage through improving energy maneuverability.

3

Given the physiological barrier, the industry began to look not

at expanding the energy maneuverability envelope but at how quickly

an aircraft could transition from one point in the envelope to

another. This school of thought guides today's agility research and

is seen as the main source of airframe related combat advantage for

at least the next generation of combat aircraft.

Improvement in aircraft agility places certain requirements

and constraints on an aircraft configuration. Proper trade studies

need to be performed at the preliminary design stage in order to

create a balanced airframe. The purpose of this project is to include

agility analysis into the ACSYNT (AirCraft SYNThesis) design code

developed at the NASA Ames Research Center. To illustrate how

agility analysis can be incorporated into the ACSYNT code a

description of how it operates must first be covered.

ACSYNT is a FORTRAN program developed as a tool to be used in

the preliminary design of aircraft. It is composed of modules that

each perform a different analysis function or analyze a separate

discipline relevant to aircraft design.

The primary modules in ACSYNT are geometry, trajectory

(mission profile), aerodynamics, propulsions, and weights. These

modules and others such as takeoff/landing and economics are each

called separately. When a module is called it then performs its

analysis and applies its constraints to the aircraft configuration.

The modules are each called repeatedly until they converge on the

solution of an aircraft configuration that can perform the specifiedmission.

4

The real power of ACSYNT is achieved when it is linked to

another NASA code called COPES. This code is a generic

optimization code. When ACSYNT and COPES are coupled,

multivariable optimizations can be performed. A large array of

variables from all modules are available to be constrained or

optimized. Typically the gross takeoff weight is optimized for the

least value. This procedure provides the lightest preliminary

configuration that satisfies mission requirements.

The main use of the ACSYNT-COPES package is to perform

trade studies of configurations and to evaluate the impact of

technologies on configurations. The improvements in materials,

propulsions and other technologies can be incorporated and their

effect on aircraft configurations can be readily determined. In this

way the feasibility and penalty of technology can be assessed.

The objective of the agility module in ACSYNT is to provide

analysis of agility metrics and, when developed, agility criteria.

Implementation of technologies to improve aircraft agility could be

analyzed and optimized in ACSYNT and their penalty and impact on

other design constraints determined. This analysis will provide

some insight into the utility of agility technologies and the combat

effectiveness of an aircraft configuration.

The objective of this study is to develop the framework for the

agility module. The basic code architecture is to be designed with

emphasis on adaptability so that many different agility metrics can

be analyzed. In addition, the code should be able to apply various

constraints for use in optimization.

CHAPTER 2

DISCUSSION ON AGILITY METRICS

The discussion on agility metrics begins with a description of

a general maneuverability diagram- the doghouse plot- and the

definition of corner speed. Their significance to agility analysis is

discussed.

The second section of this chapter is a survey of several

agility metrics developed and used by industry. Finally, the relation

between these metrics and the project scope and code architecture

is discussed. The ultimate goal of ACSYNT's agility module is to be

able to both analyze existing metrics and be adaptable enough to

analyze metrics yet to be created.

The Doghouse Plot and Definition of Corner Speed

The general character of the agility module is to operate on

the upper boundary of what is frequently referred to as the doghouse

plot. This is a graph of turn rate versus speed or Mach number.

Figure 2.1 illustrates a typical doghouse plot. The upper boundary of

this graph indicates the maximum turn rate for a given Mach number.

As shown in Figure 2.1, there is a peak in the upper boundary.

This peak represents the highest turn rate for any Mach number. The

Mach number corresponding to the peak is usually called corner

speed.

The aircraft's turn rate is limited by different constraints

depending on which side of corner speed it is flying. Above corner

5

6speed, the aircraft can aerodynamically generate a higher load

factor than the aircraft's structure can withstand. The aircraft is

said to be "load limited" with the maximum turn rate determined by

the maximum designed load factor. Below corner speed, the aircraft

is operating at its maximum lift coefficient and cannot

aerodynamically generate the design load factor. In this region the

aircraft is said to be "lift limited."

From the above discussion, the definition of corner speed can

be inferred: the Mach number that produces the maximum design load

factor at maximum lift coefficient is the corner speed.

TurnRate

Uft limitedturn

• •

Stall Comer

speed speed Mach Number

Figure 2.1

Illustration of the Doghouse Plot

Survey of Agility Metrios

This section describes several of the many agility metrics

introduced by industry. It also provides a good sample of the

spectrum of agility metrics. The uniqueness of each metric

illustrates how the different concepts of agility have produced

differing opinions on which parameters are important.

7

Combat Cycle Times

The combat cycle time metric measures the time it takes to

turn through a specified heading change and then accelerate to

regain the energy lost during the turn. The objective is to complete

this maneuver in the least amount of time. In this maneuver the

aircraft operates along the upper boundary of the doghouse plot

discussed earlier in the chapter. Figure 2.2 illustrates the path the

aircraft follows on this plot over the course of the maneuver.

t3 2

EP

t5Vc Vl

i.._

Mach Number

8

Legend:

Vl-starting and ending speedtl-time to bank into turnt2-pitch up to load factor

t3 1 -time spent in load limited turn

t32- time spent in lift limited turn

Vc-corner speedt4-pitch down to unity load factort5-roll to wings levelt6-time to accelerate back to V1

Figure 2.2

Combat Cycle Time Maneuver Circuit

Pointing Margin6

The pointing margin metric measures how fast an aircraft can

point his nose at an adversary aircraft. The two aircraft begin at

nearly the same location in space but pointed in opposite directions

(see Figure 2.3). The aircraft also begin at the same Mach number.

9

At the start of the metric both aircraft begin a maximum

acceleration turn toward one another. The aircraft that first brings

his line of sight upon the opposing aircraft's position is considered

the most agile. The measure of merit is the pointing margin or the

angle between the two aircrafts' lines of sight just as the inferior

aircraft is captured. The greater this angle the longer it takes the

losing aircraft to acquire the winning aircraft's position. This

provides the winning aircraft a longer missile flight time and a

better chance of a kill.

/_ Pointing

/ 7 sec

\Horizontal Plane

f

\

\I

I/

0 sec

Figure 2.3

Pointing Margin Agility Metric

10

Torsional agility7

Torsional agility measures an aircraft's ability to quickly

rotate the acceleration vector about the aircraft's longitudinal axis.

Its definition is simple and straightforward. For a given altitude

and Mach number, torsional agility is the maximum possible turn

rate divided by the time to perform a 90 degree roll maneuver.

Axial agility9

Axial agility measures the influence of the propulsion system

on the aircraft's ability to quickly gain or lose energy. For a given

altitude and Mach number, axial agility measures the difference

between maximum and minimum specific excess power divided by

the time for the aircraft to transition between these two power

levels, ie.

-PSmax -- "PSmin

At

For this metric not only is the transient time important but

the range of excess power levels is also important. Thus the

maximum and mimimum values of available power (engine) and

required power (airframe drag) are important as well as the ability

to quickly transition between these maximums and minimums.

Dynamic Speed Turn5

The dynamic speed turn metric does not track one specific

measurable quantity. Instead, it consists of a pair of graphs that

11relate two parameters over an entire flight envelope. The plots are

maximum turn rate versus bleed rate and the maximum straight and

level acceleration versus Mach number. These plots correspond to a

given altitude. Two example dynamic speed turn plots are

illustrated in Figure 2.4.

The bleed rate graph plots the maximum turn rate for all

possible Mach numbers versus the corresponding axial acceleration

(bleed rate). This acceleration is calculated at full thrust. The

bleed rate and the maximum level acceleration curves illustrate how

an aircraft loses energy during maneuvering and how fast it can gain

energy after maneuvering.

20 400

16A

o

(D"o

V

8

rr"

E4

I--

5O0

200 Kts

300

10 20 30 40 50

Bleed Rate (Kt/sec)

Figure 2.4a

Plot of Turn Rate Versus Bleed Rate

for the Dynamic Speed Turn Metric

12

15

o

¢o 10Vv

t-O

.e-=

o

5m

, = i J I I_100 200 300 400 500 600

Velocity (Kt s)

Figure 2.4b

Plot of Level Acceleration Versus Velocity

for the Dynamic Speed Turn Metric

Aailitv Metrics in Relation to Proi " r

The metrics previously discussed illustrate the differences of

opinion on what agility is. Some metrics analyze how efficiently

aircraft use energy to achieve an objective and also how quickly

they can regain lost energy. Other metrics analyze the quick-action

nose pointing capability of a configuration. For this project it was

decided not to select just one of these philosophies for the agility

module but to make the module adaptable enough to accomodate

several of the philosophies and their respective metrics.

13To limit the project scope, the development of the overall

architecture was considered the most important task and the

primary responsibility of this project. One metric, combat cycle

time, was used as an archetype for the development of the

architecture. This metric was selected because it contained almost

every element of the agility philosophy spectrum. While combat

cycle time's main focus is on the gain and loss of energy, it also

contains quick-action maneuvers (roll and pitch) within it. It was

therefore considered the best metric for use as an archetype for the

code architecture. Because of this selection, the complete

development of the combat cycle time metric as a separate

subroutine is included in the project scope.

The methodology used to develop the agility module

architecture is the subject of the next chapter.

CHAPTER 3

GENERALMETHODOLOGY

The overall structure of the code is a time-stepping routine

that tracks pertinent parameters over the course of the agility

maneuver. This method is basically a simulation technique.

Although many metrics, such as Lateral Agility, involve parameters

that can be solved for directly, others, such as combat cycle time

and pointing margin, require parameters that are tracked throughout

the maneuver's time interval. It is these latter type of metrics that

require the simulation methodology.

Since combat cycle time was selected as an archetype for the

simulation package there exists a separate subroutine dedicated to

analyzing this metric. To evaluate other agility metrics, one of two

options may be used. First, the main input file allows the user to

directly call the simulation package and construct the desired

metric maneuver. The second option is to create a dedicated

subroutine similar to the one for combat cycle time to conduct the

metric maneuver.

The time stepping routine tracks important parameters such as

Mach number, turn rate, and horizontal position. The time histories

of these parameters forms the bulk of the data used in metric

analysis. The final section of this chapter describes the list of

tracked variables but first some other basic characteristics of the

simulation package will be discussed.

14

15

Constant Altitude

Most of the agility metrics discussed previously involve

maneuvers that occur at constant altitude. Therefore a constant

altitude assumption was made throughout the development of the

flight mechanics. This assumption greatly simplified the resulting

equations. However, this is not to say the aircraft was constrained

to fly level. Instead, the vertical excursions were ignored. For

example, imagine an aircraft flying straight and level at constant

airspeed. If the aircraft is suddenly banked, without altering the

angle of attack, the unity load factor vector no longer counters

gravity as is shown in Figure 3.1. This results in a downward

acceleration. In the agility module, the downward acceleration was

ignored and the vertical displacement was not tabulated. However,

during the short'time of a roll, this displacement was considered

negligible.

If the purpose of the roll was to enter a level turn, the roll

segment would be followed by a pitch segment. The purpose of

pitching the aircraft would be to raise the load factor to that

required for a level turn at the given bank angle. Again, the vertical

excursion was considered negligible. This technique requires some

orchestration of the maneuver segment sequence and thus it is

somewhat the user's responsibility to ensure maneuvers are level.

Earth

f

Vertical\

\_i _ Uaba2a nced ca/ig ht v ect° r

L=W _--- T acceleration

_(t) f f J J

f/ \

\

W \

16

Figure 3.1

Downward Vertical Acceleration Due to

Unbalanced Weight Vector at a Bank Angle

Breakuo of Maneuvers Into Segments

The metric maneuvers were divided into separate maneuver

segments to simplify analysis. Each of the agility metrics

discussed previously consisted of at least one maneuver segment.

Most metrics are a combination of several segments of different

types. Figures 3.2 and 3.3 illustrate the four types of maneuver

segments; rolls, pitches, turns, and accelerations. Figure 3.3 also

shows the segments divided into two categories; functional and

transient. This classification, which is similar to the agility metric

17

classification system in reference 9, is used to separate the flight

mechanics development in Chapter 4.

Functional maneuver segments deal with long-term changes in

aircraft energy state, position and attitude. Equations of motion for

the functional segments were steady-state equations for turns and

rectilinear flight.

Transient maneuver segments deal with short-term changes in

aircraft accelerations, positions and orientation. Equations of

motion for the transient segments were standard longitudinal and

lateral-directional perturbation equations.

The functional segments, turns and accelerations, actually

represent quasi-steady turns and straight line accelerations. The

term "quasi-steady turn" refers to a steady, level turn maneuver

where the velocity may be changing. If a turn cannot be sustained

the aircraft loses airspeed. In order to maintain the load factor, the

angle of attack needs to gradually increase. Or, if the aircraft is

lift-limited and cannot sustain the load factor, the bank angle will

gradually have to decrease to maintain the level turn. These changes

in angle of attack and bank angle are gradual enough that the steady

turn equations of motion can be used and the perturbation equations

need not be employed. It is this type of turning maneuver that is

termed quasi-steady.

18

L,I-"

Accelerate

_._ Roll _,,, Pitch _lJ

FI-- FI_-_

\\

/

Roll Pitch

Tu rn

Figure 3.2

Breakup of Metric Maneuvers Into Maneuver Segments

19

Maneuver Segment Categories

IFunctional Segm ents

I ITuroII _cce,e_a,,on1 I

ITransient Segments

Pitch II

IRoll

Figure 3.3

Illustration of the Agility

Maneuver Segment Categories

Tracked Variables

In order to evaluate agility metrics, nineteen parameters

needed to be tracked. For each time step these parameters were

calculated and stored. The primary output of the agility module is a

time-stepped array of these parameters. The nineteen tracked

variables are listed in Table 3.1.

Not all of the parameters in Table 3.1 are intuitive and

therefore need explanation. Axial acceleration is the acceleration

along the velocity vector and contributes solely to velocity changes.

The throttle command is a variable whose value determines the pilot

commanded thrust level; full afterburner, full dry, flight idle, etc.

20

The thrust vector angle parameter, which is also pilot commanded,

does not represent pitch control thrust-vectoring but instead, thrust

vector rotation about the aircraft center of gravity as in powered-

lift aircraft such as the McDonnell Douglas AV-8B.

The second row in Table 3.1 involves the engine parameters.

Gross thrust represents the total installed thrust force developed by

the engine. Net thrust is gross thrust minus the momentum flux at

the inlet (ram drag). At zero airspeed gross and net thrust are

identical. As airspeed increases ram drag increases and the net

thrust developed by the engine decreases. These two parameters are

important during thrust-vectoring maneuvers. It is the gross thrust

that is vectored normal to the flightpath. The ram drag (Tg-Tn)

however, remains in the airflow (axial) direction.

The engine core percent and afterburner percent represent the

core thrust over full dry thrust and the afterburner thrust over full

afterburner thrust respectively. These parameters are not

necessarily important for flight mechanics but are important for the

throttle transient algorithm and will be discussed later.

The third row of Table 3.1 contains well known parameters.

The fourth and fifth row contain lateral-directional motion

variables and aircraft position variables, all of which will be

defined in the next chapter.

21

Table 3.1

Variables Tracked Over Time by the Agility Module

M

mach number

Tg

gross thrust

(pounds)

angle of attack

(degrees)

heading angle

(degrees)

X

downrange

distance

(feet)

axial

acceleration

(.q's)

Tn

net thrust

(pounds)

n

normal accel.

'load factor'

(9's)

turn rate

(de,cjlse¢)

Y

crossrange

distance

(feet)

Throttle

command logic

(numeric)

Engine core

thrust

(% thrust)

CL

lift

coefficient

(t)

bank angle

(degrees)

R

turn radius

(feet)

;L

thrust vector

angle

(degrees)

Afterburner

thrust

(% thrust)

CD

drag

coefficient

P

roll rate

(deq/sec)

CHAPTER 4

FLIGHT DYNAMICS

In order to evaluate the tracked variables a flight dynamics

strategy needed to be developed. First, the flight dynamics were

divided into two categories, one for the functional maneuver

segments (quasi-steady turns and straight line accelerations) and

one for the transient segments (rolls and pitches). The functional

maneuver strategy used steady state maneuver equations to develop

equations of motion. The transient maneuver strategy used lateral

and longitudinal perturbation equations of motion as developed in

reference 10 for the roll and pitch segments. These two strategies

are discussed in the last two sections of this chapter. First,

however, appropriate coordinate systems are developed and some

relevant tracked variables are defined.

Coordinate Systems

Tracking of parameters necessary to evaluate agility metrics

required three coordinate systems. The first system was an

inertial, Earth-fixed system designated (Xl, Y1, Z1). The X1-Y1

plane lies in the horizontal with the Z1 axis pointing down toward

the center of the Earth as shown in Figure 4.1. The downrange and

crossrange parameters (X,Y) referenced in the previous chapter and

listed in Table 3.1 correspond to the Xl and Y1 translations

respectively.

22

23

The second coordinate system was designated (X2, Y2, Z2) and

is also shown in Figure 4.1. This system translates with the

aircraft but does not rotate with it. As the aircraft moves the X2

axis remains parallel with the Xl axis, Y2 remains parallel with Y1,

and Z2 parallel with ZI.

The third coordinate system was designated (X3, Y3, Z3). This

system and the second system (X2, Y2, Z2) are illustrated in Figure

4.2. This third system translates with the aircraft but also rotates

laterally with it. The X3 axis remains pointed in the direction of the

aircraft velocity vector but the Y3 axis remains pointed toward the

aircraft's starboard wingtip. Since the aircraft is constrained in

altitude the velocity vector (and hence X3) must always lie in the

X1-Y1 plane.

The heading angle parameter (_) descrlbed in the previous

chapter is defined as the angle between the X2 axis and the X3 axis.

The bank angle parameter (_) is defined as the vertically projected

angle between the X2-Y2 plane and the Y3 axis. Both the heading

angle and the bank angle are shown in Figure 4.2.

At the start of a metric (t=0), all three coordinate systems

coincide with their origins at the aircraft center of gravity. All

three X axes point along the aircraft's velocity vector, all Y axes

point toward the starboard wingtip, and all Z axes point toward the

center of the Earth.

Along with each of the three coordinate axes there corresponds

a set of velocity components u,v,w and accelerations _,_, _,.

However, not all of these parameters are of interest in metric

24

analysis. Instead of a complete set of coordinate transformation

matrices, each parameter was calculated independently. This

resulted in reduced computer time.

Xl

Inertial oo_,_ _,_ _'G°Frame _

_._ _ -..._l_._-_"Translating _

I _ .--." _ _- -I _ . Frame _

Y1

Figure 4.1

Orientation of the Inertial Coordinate Frame

and the Translating Coordinate Frame

25

X2

Y3

_Y2

Y3 Z3_Z2

Figure 4.2

Orientation of the Rotating Coordinate Frame

With Respect to the Translating Coordinate Frame

Develooment of Free-Body Diaarams and Eauations of Motion for

Functional Maneuver Seaments

To develop equations of motion for the functional maneuver

segments, free-body diagrams were first created. From these

diagrams the acceleration components normal and parallel to the

flight path (X3 axis) could be determined. Figure 4.3 illustrates the

free-body diagram used to determine the parallel (axial)

acceleration component. From this diagram the force summation

results in:

,7..r,= _, (4.1)

Expanding into separate forces yields:

Tg cos(a + _) - D,,m - Dram = ax

26

(4.2)

Substituting in identities for Daero and Dram and solving for ax:

g T (4.3)

Rearranging results in the final expression for the axial

acceleration:

Tg- Tn

W(4.4)

The free body diagram in Figure 4.4 illustrates the forces that

generate the normal acceleration component. This component

consists of three separate elements: acceleration due to

aerodynamic and thrust forces, gravitational acceleration, and the

reactive centripetal acceleration. The objective is to develop

equations for the turn rate and turn radius through the centripetal

acceleration element. The centripetal element is in turn developed

from the other two acceleration elements.

For equilibrium in a steady level turn the aerodynamic and

thrust acceleration element (aF) must be balanced by the

27

gravitational (g) and the centripetal (acent) elements. The balance

constraint gives:

a2 2 g2=a_., + (4.5)

Solving for acent:

1

a_,, = (a_ - g2)_- (4.6)

The aF element is represented by:

_..,FF = m_ F (4.7)

-Tg sin(a + _,) - L = aF (4.8)

aF:

Substituting in the identity of L and solving for the component

(4.9)

Rearranging results in:

(4.10)

28

Substituting in the aF relationship into equation 4.6 produces

the final identity for the centripetal acceleration:

2t' (4.11)

Equations for the turn radius and turn rate can be determined

from basic rotational kinematics. The relationship between turn

radius, velocity and centripetal acceleration is:

V 2

a_,= T (4.12)

Rearranging gives:

V 2

R=-- (4.13)ac.tnt

Substitution of the acent identity of equation 4.11 results in"

V 2

R= 1 (4.14)

The arc length (s) of a curved flight path is defined by:

s=R_ (4.15)

29

The derivative with respect to time gives"

V=R_ (4.16)

Substitution of the R relationship of equation 4.14 results in

the turn rate equation"

f tg sin(a + _,) + qcL ]2 _ 2

V(4.17)

Dram L l Tgross

X3

Wcos_

Z3

Figure 4.3

Free Body Diagram for the

Axial Acceleration Component

• Vertical

\

Tgross sin(o_+;L) j_

Earth l_ent_

W

S

fJ

f

Horizon

\

30

Figure 4.4

Free Body Diagram for the

Normal Acceleration Component

Eauations of Motion for Transient Maneuver Seaments

Equations of motion for the transient segments were standard

lateral-directional and longitudinal perturbation equations. From

these equations standard approximations were made to achieve

simplified modal response models. The next two sections deal with

the development of roll and pitch response modeling.

31

Roll Segments

The roll segments were modeled with a single degree of

freedom, lateral equation of motion found in reference 10. This

equation models roll response given: the roll damping derivative (Lp),

aileron effectiveness derivative (L_a), an aileron deflection (Sa), and

initial conditions. The basic equation is:

f_ = Lpp + L&&a (4.18)

Construction of the dimensional derivatives in the above

equation required stability derivatives that were difficult to obtain.

No direct method was found to extract these derivatives from

ACSYNT. Therefore, the dimensional derivatives Lp and _a are input

directly by the user.

Figure 4.5 illustrates a typical roll maneuver as conducted by

the code. The control input strategy involved first deflecting the

ailerons to the user specified angle causing a roll acceleration. As

the roll progresses, and the bank angle approaches the target bank

angle, the control input is reversed. This creates a strong roll

deceleration. If this control reversal is timed properly, the roll rate

drops to zero just as the target bank angle is acquired. This control

strategy provides the quickest roll maneuver possible for a given

aileron deflection. For simplicity, step control inputs were

assumed.

The timing of the control input reversal required an iterative

technique. Once the reversal time was determined the roll rate and

32

bank angle schedules were calculated by integration of the roll

equation with the proper initial conditions. These equations were:

For roll rate during initial control input:

P(t)=P,,(1-e L'') (4.19)

where the steady state roll rate (Pss)is:

-L,._ (4.20)P"= Lp

The bank angle during initial control input is:

##(t)=#ao + p_It + l---(1--eL"))Lp (4 .21)

The roll rate after the control reversal is defined by:

p(t) = p_(2eL'(t-" ) - eLd - 11 (4.22)

The bank angle after the control reversal is:

*(,)=_0+P---(2,,('-")-,4,_1)-p.(,-2,')L,k (4.23)

where t* is the time of the control input reversal

33

AileronDeflection

(_e)

PollRate(p)

Bank Angle

(_)

I I

I

I I

I I

I I

I

I

I !t*

v

Time

t* - time of aileron

input reversal

"13me

Figure 4.5

Illustration of a Typical Roll Maneuver

Pitch Segments

The pitch equations of motion were standard two degree of

freedom short-period approximation equations as developed in

reference 10. The s-domain matrix for these two equations is:

34

r w,_z, _v,_ ljs-_l._lz,1.L-{M_+Mo} _:-M,,]/e(_)|- 1M4 [4.24)

l,_(s)J

The dimensional derivatives for the above matrix were

constructed from the standard stability derivatives. The stability

derivatives were in turn calculated from parameters found in

ACSYNT's existing code. Some of the parameters were obtained

directly from ACSYNT while others were constructed through

equations found in reference 11. These stability derivatives are:

CL,~ obtained directly from ACSYNT

cM,,~ obtained directly from ACSYNT

c,,.=-2[C,o,,lhVh(X..- X _(_ x "_

hVh(X ,-eL°. cVc(X.c•

(4.25)

(4.26)

In the last two equations, only effects from the horizontal tail

(subscript h) and the canard (subscript c) are included.

Reference 10 resolves the short-period matrix into time

responses for both angle of attack ((_) and pitch angle (E)). A typical

pitch time response is shown in Figure 4.6 These time responses are

for a step control deflection. The angle of attack starts at zero and

ends at the steady state angle of attack corresponding to the new

35

control deflection. If the o_(t) equation is considered as A(z(t), it can

be used for starting angles of attack other than zero.

The single-step input control strategy is not, however,

typically the way pilots perform pitch maneuvers. To improve the

model the o_(t) response equation was modified to include initial

conditions for (z and e. With these initial conditions included, the

response to multi-step control deflections could be constructed. A

multi-step input schedule would better model a pilot's variable

control input.

The desired pitch control input is that which provides the

quickest rotation from the starting load factor to the desired load

factor. When both the single-step and multi-step control strategies

were tested with this goal in mind, little difference in pitch

response was noticed. Figure 4.7 illustrates the close resemblance

of the pitch responses for both control strategies. Since the multi-

step control strategy increased the code complexity without

providing a significant improvement in the response model, this

strategy was rejected.

The load factor during a pitch maneuver consists of two

elements: steady state and dynamic. At any given point in time, the

present angle of attack produces a lift force and thus a load factor.

This represents the steady state element. There is, however, a

dynamic load factor element due to the pitch rate. This element was

found from reference 12. This text defines the dynamic load factor

as:

ndm(t)=V..(&-e ) (4.27)

36

When a comparison was made between load factor histories

with and without the dynamic element little difference was found.

A sample load factor response with and without the dynamic

element is illustrated in Figure 4.8. Since the dynamic load factor

element complicated the pitch coding and provided little benefit, it

was discarded from the pitch model.

The final form of the pitch model will now be restated. The

pitch model consists of a transient angle of attack time response

due to a step control input. The load factor resulting from this

control input consists of only the steady state load factor due to the

instantaneous angle of attack. This strategy provided a satisfactory

pitch transient with the least complicated and fastest computer

code.

Aircraft configurations were constrained to a pitch damping

ratio of at least 0.7. If the configuration did not have this level of

damping the derivatives Cmq and Cm_ were artificially increased to

provide sufficient damping. This constraint was employed to

approximate the effects of a flight control system that limits pitch

overshoot.

Unstable configurations were also artificially constrained. To

prevent the pitch equations from blowing up, the pitching moment

slope Cmo_ was forced to be -0.1 or less. Again, this constraint was

employed to approximate the effects of a flight control system. It

was recognized that this method was very rudimentary. However, it

was decided to use this technique in conjunction with a warning flag

37

in the output file as apposed to no pitch analysis for unstable

aircraft at all.

This procedure was considered feasible for two reasons. First,

the objective of the pitch maneuver is to move from one load factor

to another and to generate a representative angle of attack response.

Whether the angle of attack response is generated by a simple

constraint as above, or by a dedicated flight control system design

is immaterial from a preliminary design point of view. The end

result would not differ significantly.

The second reason the pitch constraints were considered

feasible is that in functional agility metrics, transient segments

like pitch contribute little to the overall maneuver performance.

Nevertheless, metric analysis where pitch response is

significant is not recommended for negatively stable configurations.

Adequate analysis for these types of maneuvers will be possible

when ACSYNT's planned Flight Dynamics Module is introduced.

38

12

10

09

8

V

(.}6

O

4

¢-<

2

00 0.5

--e--Pitch Angle

1.5 2

Time (seconds)

2.5 3

100

8O

(/)

60 _"10

E3¢-

40 <t-O

o_

13_

20

0

Figure 4.6

Typical Pitch Response to a

Step Elevator Deflection

39

10

8(/}

OI=--

O

-o 6v

O

<",-- 4O

¢.-<

2

0

0

.............T.................i................. ,_................................. i.................T.................................. P..............

i ................i......I--e--Single-Step Pitch Response I ,

i I---_-Multi-Step Pitch Response | ...................

0.4 0.8 1.2 1.6 2

Time (seconds)

i

Figure 4.7

Comparison of Pitch Response Due to

Single and Multiple Elevator Deflections

4O

8 i I I I I II I I I

I . . . I

c_

v

0

"0c_0

._/

6

4

2

00 0.4

--e--Steady State Response

---*--Steady State + Dynamic Response

0.8 1.2

Time (seconds)

1.6 2

Figure 4.8

Load Factor Pitch Response With

and Without Dynamic Term

CHAPTER 5

ENGINE THRUST TRANSIENT DEVELOPMENT

The engine transient model was based on non dimensional data

for a 1990 era low-bypass turbofan fighter engine. This data did not

contain time responses for thrust changes from any thrust level to

any thrust level, but instead, consisted of six particular throttle

responses, these responses are included in Table 5.1.

Table 5.1

Throttle Response Time Histories Obtained from Contemporary

Fighter Engine for Use in the Agility Module

Max afterburner -> Flight idle

Max dr), -> Flight idle

Flight idle -> Max afterburner

Max afterburner -> Max dry

Flight idle -> Max dry

Max dry -> Max afterburner

Figure 5.1 illustrates the time histories of these six throttle

responses. At any time step, the commanded power level may be

changed by code logic. When this occurs the proper throttle response

curve is enacted to provide a time history of the engine transient.

Throttle changes do not always fit one of the six throttle

responses. The throttle change may start or end at a partial throttle

setting instead of max A/B, max dry or flight idle. In this case, the

41

42

code begins its time history in the middle of the appropriate

response curve. Figure 5.2 illustrates an example of this technique.

The main drawback to this method is that engine response lag is not

represented in a throttle change beginning at fifty percent dry power

for example. Instead of an initial lag, the power increases rapidly

right from the beginning of the throttle change. In reality, there

would be response lag irregardless of the starting throttle level.

However, information on the engine transients was limited to the

six time of response curves so this method was employed.

Twet

Tdry

Engine

Thrust

Tidleh,._

Time

Figure 5.1a

Throttle Transient Response from

Flight Idle to Maximum Afterburner

43

Twet

Tdry

EngineThrust

Tidle

Time

Figure 5.1 b

Throttle Transient Response from

Flight Idle to Maximum Dry Thrust

Twet

Tdry

Engine

Thrust

Tidle

Timev

Figure 5.1 c

Throttle Transient Response from

Maximum Dry Thrust to Maximum Afterburner

44

Twet

Tdry

EngineThrust

Tidle

Time

v

Figure 5.1d

Throttle Transient Response from

Maximum Afterburner to Maximum Dry Thrust

Twet

Tdry

EngineThrust

Tidle

Time

v

Figure 5.1e

Throttle Transient Response from

Maximum Dry Thrust to Flight Idle

45

Twet -

Tdry,

EngineThrust

Tidle

Timev

Figure 5.1 f

Throttle Transient Response from

Maximum Afterburner to Flight Idle

Engine _- .......

T hrust

/dry se does not

' j" _ containthetypical initial lag.

Throt tie level at /,_" _'tead, thethrust increase istimeof engine -- • f- Immediate_

spool corn

man/d / "I _'_,6tandard= " response curve which isZL

Tidle]J _ i equivalent to curve in Figure 5.1 a.

to Timetirneat start of

throttle change

Figure 5.2

Throttle Transient Response Starting from

Partial Dry Throttle up to Maximum Afterburner

CHAPTER 6

CODE OPTIONS AND FEATURES

This chapter describes some of the operating features and

simulation techniques used to conduct the aircraft through an agility

maneuver. The following sections describe how the simulation

package conducts agility maneuvers and how users may manipulate

input parameters to customize these maneuvers.

Angle of Attack Limiting

The user has control of the maximum angle of attack allowable

during metric maneuvers. This limit provides a reference for

determining maximum lift coefficient. ACSYNT's aerodynamic

module does not" calculate a discrete stall angle of attack. Figure

6.1 illustrates a typical lift curve slope from ACSYNT. The lift

slope curve does not exhibit an identifiable stall break. Instead, the

slope of the curve gradually reduces to zero at extreme angle of

attack. Without an obvious stall point, the definition of maximum

lift coefficient is difficult to pinpoint. The inclusion of a user

defined angle of attack limit provides a reference for determining

maximum lift coefficient. Therefore, the angle of attack limiter is

not a user option, but a necessary input.

46

47

LiftCoefficient

Angle of At tack (degrees)

Figure 6.1

Typical Lift Curves Generated By ACSYNT

v

Definition of T_rnina SDeed

The simulation package is set up to maintain a desired

airspeed, determined by the code, called turning speed. This logic is

incorporated to keep the maneuvering aircraft in the most favorable

Mach number regime for high turn rates. There are two ways that

the code specifies turning speed. Which of these methods the code

uses to calculate turning speed depends on user input.

The primary definition of turning speed is similar to that of

corner speed discussed in Chapter 2. The turning speed is the Mach

number corresponding to the intersection of the lift-limit curve and

the load-limit curve of the doghouse plot in Figure 2.1. However,

the load-limit curve for turning speed does not correspond to the

maximum design load factor as is the case for corner speed.

Instead, the load-limit curve corresponds to the load factor

specified by the user for the turn maneuver. This makes the turning

48

speed a variable. The turning speed for a 7g turn will be higher than

that for a 4g turn. Figure 6.2 shows, for the same aircraft, various

turning speeds for different turning load factors.

The second definition of turning speed is simply a Mach number

input by the user. This allows complete control over what Mach

number the code will try to capture. The advantage of this

capability is illustrated in the following example.

Suppose a 4g turn was desired with an entry speed of Mach 0.9.

From the angle of attack limit and the 4g load factor, the code

calculates the turning speed to be Mach 0.35. For the Combat Cycle

Time metric it would not be desirable for the code to decelerate the

aircraft down to Mach 0.35 for the turn. Although the turn rate

would be increasing and the turn would be completed earliest, the

re-acceleration phase would be much longer. To minimize total time

it would be best to turn at a higher airspeed. The lower turn rate

would lengthen the turn segment, but the acceleration back to Mach

0.9 would be much shorter for an overall quicker cycle time. Thus,

allowing the user to set the turning speed at Mach 0.65 or so, a

better maneuver performance can be achieved.

49

TurnPete

Lift limit- CLmax

Lo>,,m,

Stall I I 7g turning speed Mach numberSpeed

I 5g tu r ni ng speed

3g tur ni ng speed

Figure 6.2

Variation of Turning Speed

With Turning Load Factor

Throttle Control and Turnino Soeed CaDturo

The simulation package maintains turning speed through

throttle manipulation. In order to achieve this the user inputs

throttle settings that refer to the throttle power settings discussed

in Chapter 5. There are two throttle settings for each maneuver

segment; one setting is for airspeeds above turning speed and the

other for airspeeds below turning speed. By commanding a low

power level for the above-turning-speed throttle setting, the

aircraft can be controlled to decelerate back down to turning speed.

Conversely, by commanding a high power level for the below-

turning-speed throttle setting, the aircraft can be controlled to

50

accelerate back up to turning speed. Figure 6.3 illustrates how the

code switches throttle commands during acceleration and

deceleration through turning speed.

Mach

number

startingMach

turningspeed

Throttle command changes here, and inthis case the aircraft begins to re-accelerate

Above-turning-speed throttlesetting is commanded

Below-turning-speed throttlesetting is commanded

hiv

Time

Figure 6.3

Illustration of Throttle Control Logic asAircraft Passes Through Turning Speed

Another input parameter can be used to alter the throttle

command technique described above. This parameter is called MLEAD

(Mach number LEAD). The value of MLEAD is used as a buffer zone

around the turning speed. It causes the code to change throttle

settings before the turning speed is actually achieved. In this way

MLEAD serves as a pilot's anticipation of the approach of turning

speed and his early throttle change. Figure 6.4 shows how the

51

parameter MLEAD affects the throttle command schedule. When the

aircraft's Mach number is above turning speed+MLEAD, the above-

turning-speed throttle command is selected. When the aircraft's

Mach number is below turning speed-MLEAD, the below-turning-

speed command is selected. In the region between these two Mach

numbers (turning speed+MLEAD and turning speed-MLEAD) the

throttle is changed to whatever thrust level is required to sustain

the turning speed at the desired load factor. If the turn is not

sustainable then the thrust is set at the maximum afterburning

setting.

52

Mach

number

turningspeed

P1

P2

MLEAD>0: (bold plot ) throttle changes at P1, and inthis example, turning speed is bettercaptured by the early throttle change

MLEAD=0: (thin plot) throttle changes at P2 (right at

turning speed) which results in poor capture

Ih,..-

Time

Figure 6.4

Illustration of Throttle Control Logic When

the MLEAD Parameter is Employed

Thrust Vectoring

The thrust vectoring capability of the agility module does not

include pitch control thrust-vectoring. Instead it includes the

ability to rotate the thrust vector out of the fuselage axis yet

remain centered at the aircraft's center of gravity. This is intended

to model the in-flight direct-lift capability of aircraft such as the

Hawker Siddeley Harrier and McDonnell Douglas AV-8B. This

capability allows the aircraft to generate some of the turning load

factor through the engine. This results in higher turn rates for a

53

given aerodynamic load factor. However, this reduces the aircraft's

ability to combat drag since the axial component of thrust is

reduced.

The thrust vector angle (X) is defined as the angle between the

aircraft's fuselage axis and the thrust vector. Figure 4.3 illustrates

the thrust vector angle definition. The angle can range any where

from zero to one-hundred-eighty degrees. The transition rate (_.) is

another user input, and the transition is modeled linearly.

The user has control over the thrust vector angle during each

maneuver segment. Each segment has two vector inputs, one setting

for operation above turning speed and one for operation below

turning speed. This two-setting technique for each segment allows

the user to better model a pilot's control technique than a simple

single setting would. Similar to the throttle control, the two-

setting thrust vector control also assists in maintaining the

aircraft's turning speed.

The code user has the option of employing an airbrake during

metric maneuvers. The user inputs an equivalent flat plate area for

the extended airbrake and this drag is included with the aircraft's

clean drag. Once the airbrake option is selected, the control and

operation of the airbrake is automatic. The airbrake is

automatically extended when the aircraft is flying above turning

speed and, conversely, the airbrake is automatically retracted when

the aircraft is below turning speed. The retraction sequence was

54

assumed to be instantaneous and retraction or extension occurs over

one time-step.

External Stores Release and Weight/Moment of Inertia Control

At the start of an agility metric, the user specifies the

desired percent fuel load. This percent includes both the internal

and any external fuel the aircraft may be carrying. In addition, the

user specifies the external stores and ammunition loading of the

aircraft. The weight and drag of these stores is specified in the

weight and aerodynamic input files of ACSYNT. The moment of

inertia for the aircraft with pylons, as well as the incremental

moments of inertia for fuel and stores is specified in the agility

input file.

During any of the following maneuver segments the agility

module has the capability of dropping stores. Each segment

contains logical drop flags for four types of stores; missiles, bombs,

external fuel tanks, and ammunition.

A segment's drop flags cause the store's weight and moments

of inertia to be subtracted from the aircraft's. In addition, the

additional drag due to these stores is also subtracted from the

aircraft. The change in weight and moments of inertia as

commanded by a segments drop flags is activated at the end of the

maneuver segment.

When the user inputs the dimensional derivatives for the roll

maneuver segment they must be referenced to a moment of inertia.

For the agility module, they must be referenced to the moment of

55

inertia of the clean aircraft without fuel and without stores. In

addition, the incremental moments of inertia due to the individual

stores and fuel must be entered. With this information the code

ratios the dimensional derivatives to account for the changes in

weight and moments of inertia. The roll response is thus dependent

on the aircraft fuel and stores loading.

CHAPTER 7

CODE VERIFICATION

Code verification consisted of two phases. The first phase

was to test code logic and to ensure continuous, believable time

histories of the tracked variables. This phase tested mainly the

integrity of the code. The second phase was to compare the agility

module's maneuver analysis with the combat analysis capability

already contained in ACSYNT's trajectory module. This phase would

ensure that the agility module was retrieving aerodynamic and

propulsive data properly and that the physical equations used for

maneuverability analysis (equations 4.4, 4.14 and 4.17) are at least

consistent with an independent performance package NASA has used

for years.

The combat analysis in ACSYNT's trajectory module generates

the sustained and instantaneous turn rates, turn radii, specific

excess power and lift and drag coefficients for a given Mach number

and altitude. This information allows comparison of these

parameters with the agility calculations at an isolated time step.

A third verification phase that was not performed would be to

compare the agility analysis with actual flight test data for a

specific fighter aircraft. The reasons this was not conducted are

twofold. First, obtaining the type of information required to

perform a reasonable comparison was extremely difficult. Most

aircraft data consisted of the type described above: sustained and

instantaneous turn rates, turn radii, specific excess power for a

56

57

given Mach number and altitude. Information on how long it took to

perform an actual turn was not found. The second reason this phase

was not conducted was that the agility module relies entirely on the

aerodynamic and propulsion modules for information. Any

discrepancy in the aerodynamic or propulsive model would manifest

itself in the agility analysis.

Thus the verification was limited to the first two methods

described. The following two sections detail these verification

procedures.

Continuity of Tracked Variables

The first step in validating the code was to ensure that all

tracked parameters were continuous over the logical operating range

of the input parameters. Various maneuver segment sequences were

conducted to verify that the tracked variables remained continuous

through multiple turns, and various pitch and roll maneuvers.

In addition, the code features described in Chapter 6 were

tested thoroughly. The angle of attack limiter, airbrake, turning

speed capture and thrust-transient model all performed as designed.

All glitches found were corrected and from this verification phase

the integrity of the coding technique was considered satisfactory.

Agreement With ACSYNT's Combat Analysis

The second phase of verification involved coordinating the

agility module maneuvers with the combat phase analysis in the

trajectory module. Verification consisted of comparing the agility

58

module's sustained and instantaneous turn rates, radii, excess

powers, angles of attack and lift and drag coefficients with those of

the trajectory module. This correlation was performed over a range

of Mach numbers that covered both lift limited and load limited

flight regimes. Tables 7.1 through 7.3 catalog the comparison data

and the descrepancies. The greatest deviation was found to be three

percent. The source of this small error was attributed to roundoff

error. As an example, information from the trajectory module at

Mach 0.73 were compared to agility information at Mach 0.735. This

was about as close of a Mach number correlation as could be

performed. The agreement nevertheless was considered excellent

and proof of the codes validity in determining maneuver performance

at an isolated time step.

From the above discussion it may sound like ACSYNT can

already do what the agility module does. However, the combat

analysis in the trajectory module conducts its analysis at a frozen

instant in time. The agility module performs these calculations for

consecutive time steps and calculates the resulting kinematics

between these time steps. In this sense it flies the aircraft through

a maneuver and tracks the pertinent parameters for agility analysis.

The verification procedures indicated that the agility module

performs time dependent maneuverability analysis properly. This

procedure also indicates that the time-stepping simulation package

is an effective method of tracking an aircraft's performance

throughout a manuever.

59

Table 7.1

Correlation of Agility Module Parameters with Parameters

Calculated in COMBAT Phases of the Trajectory Module at Mach 0.73

Altitude: 15,000 feet

Parameter

Mach number

COMBAT

(ACSYNT)

.730

Agility

Module

.735

Percent

Difference

0.68%

Angle of attack 15.0 15.0 0%

Load factor 6.87 6.97 1.46%

Turn rate 16.24 16.4 0.99%

Lift coefficient 1.196 1.198 0.17%

.3986Drag

coefficient

Specific excess

power

Turn radius

.4060

-1,119

1.86%

-1,094

2,723

2.29%

2,711 O.44%

60

Table 7.2

Correlation of Agility Module Parameters with Parameters

Calculated in COMBAT Phases of the Trajectory Module at Mach 0.68

Altitude:

Parameter

Mach number

Angle of attack

Load factor

Turn rate

Lift coefficient

Drag

coefficient

Specific excess

power

Turn radius

15,000 feet

COMBAT

(ACSYNT)

.680

9.79

4.09

10.18

0.820

.1631

0

4,047

Agility

Module

.676

9.93

4.09

10.40

0.8279

.1668

-7.19

3,928

Percent

Difference

0.59%

1.43%

0.0%

2.16%

0.96%

2.27%

N.A.

2.94%

61

Table 7.3

Correlation of Agility Module Parameters with Parameters

Calculated in COMBAT Phases of the Trajectory Module at Mach 0.53

Altitude: 15,000 feet

Parameter

Mach number

Angle of attack

Load factor

COMBAT

(ACSYNT)

.530

Agility

Module

Percent

Difference

.534 0.75%

15.0 1 5.0 0%

3.47 3.52 1.44%

1 0.93 11.02 0.82%Turn rate

Lift coefficient

Drag

coefficient

Specific excess

power

Turn radius

1.119

.3458

-176

1.121

.3540

-181

0.18%

2.37%

2.84%

2,937 2,896 1.40%

CHAPTER 8

EXAMPLE STUDIES

In this chapter the influence of two parameters, thrust loading

and wing loading, on the Combat Cycle Time metric are investigated.

In addition, an example using the COPES optimization code in

conjunction with ACSYNT to optimize the wing loading and thrust

loading for minimum gross takeoff weight is presented. These

studies are intended to illustrate how the agility module may be

used to ascertain and optimize an aircraft configuration's agility

potential. The two parameters were chosen because they are

fundamental in classical energy maneuverability analysis. In these

studies however, the new agility metric analysis will show that

aircraft that appear to have similar energy maneuverability

performance levels can have quite different levels of agility; at

least as agility is defined by the Combat Cycle Time metric.

The baseline aircraft used for the studies was a fighter

aircraft similar to a Northrop F-20 Tigershark. A three-view of this

aircraft is shown in Figure 8.1. The weights, external dimensions

and installed thrust were matched to obtain a representative fighter

model. More information on this model is contained in the appendix.

The metric studied was Combat Cycle Time as defined in

Chapter 2. The maneuver used for this metric was a 7g turn through

180 degrees at an altitude of 15,000 feet. The aircraft began the

maneuver in straight and level flight at Mach 0.9. The values for

other pertinent input parameters are also contained in the appendix.

62

63

Figure 8.1

Northrop F-20 Tigershark Three View

Effect of Thrust Loading on Combat Cycle Time

This section illustrates how the ACSYNT agility module can be

used to study the influence of an aircraft's thrust-to-weight ratio

on the Combat Cycle Time (CCT) metric.

The Combat Cycle Time maneuver was performed using the

baseline fighter configuration. For comparison, four other

configurations were flown through the same maneuver. These

configurations were altered only in the available level of thrust.

The thrust levels were specified as a percentage of the baseline

configuration's available thrust. The four percentages were 80%,

90%, 110%, and 120%. These choices were selected to bracket the

baseline configuration. The full power thrust loading of the baseline

64

configuration was 0.94. For the 80% and 120% thrust aircraft this

corresponded to thrust Ioadings of 0.75 and 1.13 respectively.

Although only the thrust level was changed and all other input

parameters were held constant, convergence of each aircraft during

ACSYNT execution resulted in slight variation in aircraft weight.

This resulted in a maximum difference in wing loading of 78.3 for

the 80% thrust configuration and 78.5 for the 120% configuration.

Figure 8.2 illustrates the time differences for each segment of

the CCT maneuver for all five configurations. As would be expected,

the highest thrust aircraft performed the maneuver in the least

amount of time. The maneuver times also steadily decreased with

increased available thrust. However, inspection of the separate

maneuver segments reveals that the lowest thrust aircraft

completed the turn segment slightly quicker than the higher thrust

aircraft. Again this trend is consistent for all five aircraft; each

turned slightly quicker than the next higher thrust aircraft and

slightly slower than the next lowest thrust aircraft. The reason for

this phenomena can be explained by looking at the time histories of

Mach number and turn rate for the five aircraft.

Figure 8.3 plots the Mach number over the course of the CCT

maneuver for the five configurations. The initial acceleration of

each configuration is due to the engine spool-up at the start of the

maneuver. Once the aircraft has completed the roll into the turn and

has pitched up to the turning load factor the increased induced drag

overpowers the thrust increase and the aircraft begin to decelerate.

65

The greatest deceleration naturally corresponds to the aircraft

with the least available thrust (80%). As the available thrust

increases up to 120%, the peak velocity deficit is reduced. The

reduced velocity deficit coupled with the more powerful engine

created significantly shorter acceleration times for the higher

thrust configurations.

The turning speed for the five aircraft was Mach 0.74. Over

the course of the turn only the 80% thrust configuration crossed this

speed. The 90% thrust configuration barely reached turning speed

just as it ended its turn. Recalling that the turning speed is where

an aircraft can generate its highest turn rate, it is understandable

why the lower thrust aircraft completed their turns sooner. Their

higher decelerations placed them in speed regimes with higher turn

rates than the greater thrust aircraft and thus were able to achieve

superior turns.

The turning performance is evident in the plots of turn rate

versus time in Figure 8.4. The lower thrust aircraft indeed have a

higher turn rate at any given time and thus out turn the higher thrust

configurations. It was observed that only the 80% thrust

configuration achieved turning speed. This can be seen in the turn

rate plot. The 80% thrust configuration reaches a peak turn rate

around 12.5 seconds. After this the turn rate drops off as the

aircraft decelerates past turning speed. At this time the aircraft is

lift limited and cannot aerodynamically generate the full seven g's.

This would suggest that during a continued turn through 270 or 360

degrees the lower thrust aircraft would lose its turning advantage

66

and fall behind the higher thrust configurations. In addition, if the

starting velocity were below the turning speed, the higher thrust

aircraft would be better able to accelerate to and maintain the

turning speed. It is situations like this that make the development

of agility criteria so difficult. The optimum configuration can be

entirely dependent on the specific situation.

An additional comment on Figure 8.4 is the overshoot evident

at the end of the pitch up (t=3 seconds) and pitch down (t=15

seconds) segments. These are due to the dynamic response model of

the pitch maneuvers. Although a minimum damping level was

specified there was still some overshoot.

Figure 8.5 illustrates the turn profile in the horizontal plane

of the maneuver. These plots are what the jet contrails of the

aircraft would look like to an individual watching overhead. The

lower thrust configurations turn tighter and possess a positional

advantage over the course of the turn segment. However, as the

aircraft accelerate back to the starting velocity the lower thrust

aircraft take longer and by the time the maneuver is completed they

have lost their positional advantage.

Figure 8.6 shows the load factor of the five configurations

over the time of the maneuver. The main interest in this figure is to

note the consistency of all five configurations. Each aircraft

follows almost exactly the same curve over the course of the

maneuver. From this graph, which is a typical of traditional

maneuverability analysis, the configurations appear to have the

same level of performance. However, as previous figures and

67

discussion illustrate, the performance of these configurations is not

identical. It is the time dependent performance of the

configurations that conveys their agility potential; at least as far as

defined by the Combat Cycle Time metric.

What is the overall conclusion of the impact of thrust loading

on Combat Cycle Time? It depends entirely on what is considered

most important. For the specific maneuver studied, the lower thrust

configurations possessed a positional advantage up to the end of the

turn segment. After this, the advantage was lost and the higher

thrust aircraft possessed the advantage. For time considerations

the higher thrust aircraft appeared to win across the board. For

longer turns of 360 degrees, the lower thrust aircraft would most

certainly lose. The general consensus would probably lean toward

increased thrust. However, the study has alluded to the tradeoff of

what type of performance is most crucial and what are its costs.

68

30

2503

"10t-Oo 2003

v

{9E

_ 15

*..10

e_

E00

5

0

T/W= 80% T/W= g0%

[] Roll [] Pitch

[] Pitch [] Roll

[] Turn [] Accel

Baseline

(100%)

BII

T/W= 110% T/W= 120%

Figure 82

Combat Cycle Time Variation

for Different Thrust Loadings

69

0.95

0.75

0 4 8 12 16 20 24

Time (seconds)

Figure 8.3

Mach Number Time Histories

for Different Thrust Loadings

70

20

16

_12

#- --_o.9_ I4 ...............................---e--baseline _

/ +,.,o t---e-- 1.20

0 i0 3 6 9 12 15 18

Time (seconds)

Figure 8.4

Turn Rate Time Histories

for Different Thrust Loadings

71

8o0o L w t -j___.._. t j

7ooo...............................................i..............................°......................"_'6000

_oooIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIIIIIZZIIIIIIZZZZIZZZZIIIIIIIZ.._....!.._,ooo_.........-_o.8o ..........i.........................i.........................i.........................i..................._r_ooo_.........+0.9o ...........!........................._.........................i.........................i...................-_

---e--baseline i .............................i..............._...-.'_..

_ooo!_.........-_-1.1o ..........._............................................................................/ t_ooo_.E.........+,._o ..........._..................................................!........._ ..............to. i i _- , ,

-8000 -6000 -4000 -2000 0 2000 4000 6000

Downrange Distance (feet)

Figure 8.5

Horizontal Plane Turn Diagrams

for Different Thrust Loadings

72

8

7

6

2

00

baselin_

.20

4 8 12 16 20

Time (seconds)

Figure 8.6

Load Factor Time Histories

for Different Thrust Loadings

73

Effect of Wing Loading on Combat Cycle Time

This section illustrates how the ACSYNT agility module can be

used to study the influence of an aircraft's wing loading on the

Combat Cycle Time metric.

Combat Cycle Time maneuvers were performed using four

different wing Ioadings for comparison with the baseline

configuration. The selected wing Ioadings were 65, 70, 85, and 90

pounds per square foot (psf). These choices bracketed the baseline

which had a loading of 78.4 psf. The wing loading was the only

change in configuration for this study. All other input parameters

were held constant. However, convergence of the aircraft during

ACSYNT execution resulted in some weight disparity. This resulted

in a slight difference in thrust loading for the five configurations.

The extremes of this disparity were a thrust loading of 0.96 for the

65 psf wing loading configuration and 1.00 for the 90 psf

configuration.

Figure 8.7 illustrates the time differences for each segment of

the Combat Cycle Time maneuver for all five configurations. The

total time to complete the maneuver was very similar for all

configurations. There was, however, a difference in the times for

each maneuver segment. The higher loaded aircraft completed the

turn segment slightly faster than the less loaded configurations.

Conversely, the higher loaded aircraft required longer accelerations

times than did the less loaded aircraft. The explanation for this is

again found in the time histories of the Mach number and turn rates

for the configurations.

74

Figure 8.8 plots the Mach number over the course of the CCT

maneuver for the five configurations. As was the case in the

previous study, there was an initial acceleration phase due to engine

spool-up until the aircraft rolled into the turn and pitched up to the

turning load factor.

In order to generate the 7 g's for the turn the higher loaded

aircraft needed to produce higher lift coefficients. This in turn

increased their induced drag. The result was the greater the wing

loading the greater the deceleration and the resultant velocity

deficit. This explains the longer acceleration phases of the higher

loaded configurations.

The greater deceleration also allowed the higher loaded

configurations to approach their turning speeds. Similar to the

previous study, the quicker approach to turning speed provided

higher turn rates. This explains why the higher loaded aircraft

completed the turn in a shorter amount of time.

In the case of different wing Ioadings the approach to turning

speed is more pronounced. Since the wing Ioadings were different,

the turning speed for each configuration was different, The

horizontal lines in Figure 8.8 designate the turning speed for the

various wing Ioadings. As the wing loading decreased the turning

speed decreased as well. This along with the reduced deceleration

of the less loaded aircraft kept these aircraft far from their optimal

turning speeds. Figure 8.8 illustrates that the lower the wing

loading the greater the difference between the turning speed and the

minimum speed obtained during the entire maneuver. Only the 90 and

75

80 psf aircraft ever reach turning speed while the 65 psf aircraft

never came within Mach 0.12 (17%) of its turning speed.

The differences in turn rate are illustrated in Figure 8.9. Here

it can be seen that as the turn progressed a higher loaded aircraft

produced a turn advantage over a less loaded aircraft. However, as

soon as the turning speed was passed the now lift limited aircraft

lost its turn rate advantage. For extended turns the higher loaded

aircraft would eventually lose the turn advantage but in this case it

still completed the turn first.

Figure 8.10 plots the turn profile in the horizontal plane of the

maneuver. This graph shows the higher loaded aircraft had tighter

turn radii. Not only did the higher loaded aircraft have a turn

advantage in terms of time but they also held a spatial turn

advantage. By the time the entire maneuver was completed and the

aircraft had re-accelerated to the starting velocity all five

configurations flew roughly abreast one another. Yet the higher the

wing loading the tighter the ending position.

Figure 8.11 shows the load factor time history of the five

aircraft. As in the thrust loading study all five configurations had

very similar time histories. The only difference is the time of

pitch-down for the five cases and the upper right-hand corner of the

90 psf aircraft. Since this configuration achieved its turning speed

and became lift limited, the load factor dropped off toward the end

of the turn. This again illustrates the importance of time dependent

performance analysis as the load factor plot shows little

discrimination between the five aircraft.

76

The overall conclusion for this particular maneuver is that

higher wing loading improves turn performance with little

detrimental impact on Combat Cycle Time (remember total maneuver

times were very similar). However, it was illustrated that the

results of this study were highly dependent on the particular type of

maneuver. Had the turn been extended to 270 or 360 degrees the

higher loaded aircraft would have lost its turning advantage and

created an excessive velocity deficit that would lengthen the

acceleration phase. This again reinforces the difficulty in

developing robust agility criteria that provide the best overall

performance for a variety of situations and tasks.

77

30

25t_

"10t-O¢.,}• 20

V

E°_

I- 15

0

o.-. 10

E0

5

0

f ................................ i

! ![] Roll [] Pitch

[] Pitch [] Roll

[] Turn [] Accel

.°.°°.°°...°.,..°..o........°..°..-.°.°...°...°.°°°..°°°o°°°°°-.O°OoO°.°O°°o°..°°.°o.°°°°°.°-°O°°oo°o°°°°°O°°o°°,°°O°.o.°°.°o-...O.°oO.°.°°°°

°°.°o°°°°o°°°°°°-.-.o.o.°°.°

°o°°°o.°°°..o°-.-.°°°°°°°°o°oo-°Oo°°°.o°.°-°°°.°°°°°.°.°°°°°Oo.o°°°°°.

;-....,.,..;...=°,°°°..,o°o,o°,.,.°=..o°-,°°,,..oO..°,°°°,,-

• .°o°.'.'°°.". ........• °......°°°..° ...°.°°°...°.. .°....o-..°.. ........°°_°°.°°.°°.°° _°°.°.°°°°.°o., ...... ° °°°.°°'°°...°.

....... ...o.o°.,,=o== ,,.-.,.-o..-.°. .o°.O=,°°.,,Oo

: :':':':':'1 "." • ".'.'." ..... • ".'. "." :':':':':':':"

o.o.o°.°°°°... .,°°°.o°o..,°°° °,°-,o°=,o.°°° .°,,o,.,.°.,,°o.,.......°... .o°....,,o°o,.O °.o-.O,,°-°°.. o°.°,°.°.*°°.,°.o.-,-..°-.-. -,.,.°°,-°°,-.= o°o°,, ,o=,..o ..,-.°.,.,°,o°.... ° .... °*°,.-.-.*..- ...°,,°.o°,,., .°.-.-.-.,°.o,

°o.,°*°=°°=°°. .,°.°.,**,.=,°° *.°,.,.,°.°°.° .,..*.°,.=.,...o°.°,°=,==°=. ,=,°.°==°O..o.o ..o..,-.,.-... ,°°.*°,o*..,-,

°=.,..o°..=°o° ,...=**°°=°.o.= .,o°.O,0..,°,° ..°°...o°=..=.,• .o°.O,°,°.°° • . • • ° • • • , • ....... • = • • ••............. :.:.:,:.:.:.: :.:.:.:.:.:.:. :.:-:.:.:.:.:,:•....,•....... ...°.,........ .:.:,:.1.:.:.:::::::: ::::::: _ _::: ;i!i_i_i_i:i_!!

W/S= 65 W/S= 70 Baseline W/S= 85 W/S= 90

(784)

Figure 87

Combat Cycle Time Variation

for Different Wing Loadings

78

EZ

.C:

0.95

0.85

90 Tuminq _peed

....A65

+70

--e-B ase l in e

i

0.7 i i

o6s I I0 4 8

Time

I12

(seconds)

I16 20

l

24

Figure 8.8

Mach Number Time Histories

for Different Wing Loadings

79

20

16

4

0

0 3 6 9

Time (seconds)

12 15 18

Figure 8.9

Turn Rate Time Histories

for Different Wing Loadings

80

8000

7000

60OO

--.-_5000

0

4000,w

a

3000c

o 2000O

1000

0

-4000 -2000 0 2000

Downrange Distance(feet)

4O00 6000

Figure 8.10

Horizontal Plane Turn Diagrams

for Different Wing Loadings

81

8

7

6

2

00

base

4 8 12

Time (seconds)

16

65

20

Figure 8.11

Load Factor Time Histories

for Different Wing Loadings

82

Use of Combat Cycle Time as a Constraint In Aircraft O.Dtimization

This section illustrates how the agility module can be used in

configuration optimization. This capability is the real power of

ACSYNT and it is these types of optimization studies that will be

used to determine the impact of agility technologies and constraints

on the overall aircraft configuration. The overall optimization

technique will first be discussed and then the particular example

will be presented to illustrate the optimization opportunities of the

agility module.

The basic optimization method used by COPES in conjunction

with ACSYNT consists of an objective variable, design variables and

constraint variables. The objective variable is the parameter that is

being optimized and can be either maximized or minimized. Design

variables are the parameters whose values are varied to provide a

design space. These design variables are given upper and lower

bounds. The constraint variables are parameters that further limit

the design space. In the case of ACSYNT typical constraints are

mission range or a sustained turn requirement at altitude. Only the

design variable space that satisfies all constraints can provide

possible solutions. The optimizer evaluates aircraft configurations

over this design space and attempts to find the design point that

produces the desired extrema of the objective variable.

In this example the objective variable was gross takeoff

weight. Naturally the objective was to minimize the takeoff weight.

The constraint for this optimization was to complete the same

Combat Cycle Time maneuver used previously within 20.00 seconds.

83

The design variables were the wing area and engine size. Table 8.1

lists the design variables bounds, the constraint variable value, and

the pertinent parameters of the starting configuration and the

optimized configuration. This information is also illustrated in

Figure 8.12.

The tradeoff in this case is wing loading versus thrust loading.

A decrease in wing loading allows a decrease in thrust loading and

vice versa. However, a larger wing adds weight to the vehicle.

Conversely a larger engine also adds weight. These two trends are

the source of the tradeoff. Some combination of wing and engine

size will satisfy the agility constraint and provide the overall

lowest takeoff weight. From Table 8.1 and Figure 8.12 it can be seen

that the trends drive the wing to as small a value as possible. This

resulted in only a moderate increase in engine size. Evidently the

agility criterion is much more sensitive to engine size than wing

loading.

The lower boundary on wing loading was reduced to see where

the wing size would stabilize. As it turns out, the wing continued to

shrink all the way down to 90 square feet. However, this portion of

the design space is really irrelevant. The only constraint applied

was the Combat Cycle Time maneuver. Any functional aircraft

configuration would have many more constraints such as takeoff and

landing performance. These constraints would require a much more

reasonable wing size. This example does show, however, the

capability of ACSYNT to use agility constraints in configuration

optimization.

84

One note on the engine size variable: the engine deck used had

an engine much larger than needed for the baseline aircraft. ACSYNT

provides a parameter called engine scale factor (ESF) that

"rubberizes" the engine. This parameter proportions the engine

thrust, airflow, fuel flow and dimensions. The engine scale factor

required to match the engine deck with the thrust level of the

baseline aircraft was 0.438 (43.8%).

85

Table 8.1

Design Space Boundaries and Final Results

for Combat Cycle Time Optimization

Desian and Constraint Variable Boundaries

Design variable

Wing area (ft 2)

Engine scale factor

LO_v_eL_b. .u

150.0

0.200

250.0

1.00

Constraint variable

Combat Cycle Time (sec.) 5.00

ODtimization

Configuration:

Combat Cycle Time (sec.)

Wing area

Engine scale factor

Takeoff weight

Results

Oriainal

21.40

200.0

0.420

19,234

20.00

150.0

0.438

18,904

86

O ""

LL _

O EO0J-

o_ ,A.C ot_-t- II

W _W

1.0

0.8

0.6

0,4'

0.2--

min

Optimization Space

POptimized Point_"'_ Starting point

j W= 15610 Ibs. W= 15,941 Ibs.CCT= 20.00 sec. CCT= 21.40 sec.

/

I

!150

I I I200

Wing Area (square feet)

max

I

_L _ _ max

I

I

I

I

I

I

I

L _ _ min

I

250

Figure 8.12

Optimization Path for Minimization

of Aircraft Takeoff Weight

CHAPTER 9

CONCLUSIONS AND RECOMMENDATIONS

This project involved designing the overall architecture of the

module and developing the quasi-simulation subroutines. While this

is the core of the agility module it is not the entire package. This

chapter will summarize the present state and capabilities of the

module and suggest future work efforts.

The present agility module is in working order and should be an

effective tool in analyzing an aircraft configuration's agility

potential. The example studies of the effect of thrust loading and

wing loading illustrate how the module can be used to perform trade

studies on parameters important to agility metrics.

The module is also capable of providing constraints for

ACSYNT's optimization capability. Once agility criteria have been

developed the module can be used to optimize an aircraft

configuration for agility requirements as well as contemporary

mission requirements.

The present module is best suited for functional type metrics.

It is particularly suited to metrics such as combat cycle time,

pointing margin, and dynamic speed turn. Although the transient

metrics may be analyzed and the architecture is well suited for

transient maneuvers, the analytical models are not as robust as for

the functional type segments. However, once ACSYNT is capable of

generating stability derivatives and the flight control module is

87

88

incorporated, the transient maneuver analysis capabilities may be

improved.

One major concern in the code development was computer run

time. A time stepping simulation with numerous tracked variables

could produce a lengthy run time, especially for functional long-

term maneuvers. However, certain measures were taken to reduce

computer time. As stated in Chapter 4, the analytical models of the

transient pitch and roll maneuver segments were simplified as much

as possible. When the added complexity of multi-step control

response and dynamic load factors provided little difference in time

response, these elements were dropped from the model. The amount

of time ACSYNT spent in the agility module was found to be about

30% greater than most of ACSYNT's other modules. While this is

definitely added length, time was reduced as much as possible

without hindering analytical performance.

The agility module's architecture has an important

characteristic for future improvements. Since industry has not yet

settled on a single definition of agility, an accepted group of

metrics, nor quantifiable requirements, the adaptable architecture

will allow future metrics and requirements to be incorporated with

the least amount of rework. The simulation's time-stepping

technique of analysis and the menu list of maneuver segments should

allow the necessary adaptability.

Future work efforts should involve development of subroutines

dedicated to performing specific agility metrics. Presently, combat

cycle time is the only dedicated subroutine. References 6,7,9 and

89

13-17 discuss many of the agility metrics developed by industry.

Most of these are appropriate for inclusion in the agility module.

Another task for future work is to continue the verification of

the routine. A comparison between actual flight test data and the

agility module would better prove the integrity of the code. The

requirement for this comparison is flight test data for a particular

aircraft performing a maneuver close to a metric maneuver.

Complete time histories for relevant parameters such as Mach

number, turn rate and spatial position would be needed.

ACSYNT does not have the capability to analyze maneuver flaps

that change their deflection over the course of a maneuver. Thus the

correlation of flight test data with the agility module should be

done with caution since most contemporary aircraft employ variable

geometry during maneuvers. For the first comparison, an older

aircraft without variable geometry would be best.

REFERENCES

• Gilbert, William P., et al. "Control Research in the NASA High-

Alpha Technology Program." AGARD Conference

Proceedings AGARD-CP-465. Symposium of the Fluid

Dynamics Panel. Madrid, Spain. October 2-5, 1989.

. Wanstall, B., and J.R. Wilson. "Air Combat Beyond The Stall."

Interavia Aerospace Review, Vol. 45, May 1990, 405-407.

o Herbst, Wolfgang B. (MBB). "X-31A." SAE Paper 871346. SAE

Aerospace Vehicle Conference. Washington, DC. June 8-

10, 1987.

. Dorn, M. "Aircraft Agility: The Science and the Opportunities."

AIAA Paper AIAA-89-2015. AIAA/AHS/ASEE Aircraft

Design, Systems and Operations Conference. Seattle,

Washington. July 31 August 2, 1989.

. McAtee, Thomas. "Agility in Demand." AerosDaoe America, May

1988, 36-38.

90

. Tamrat, B.F. "Fighter Aircraft Agility Assessment Concepts

and Their Implication on Future Agile Fighter Aircraft."

AIAA Paper AIAA-88-4400. AIAA/AHS/ASEE Aircraft

Design, Systems and Operations Meeting. Atlanta,

Georgia. September 7-9 1988.

. Skow, A.M. "Agility As a Contribution to Design Balance."

AIAA Paper AIAA-90-1305. AIAA/SFTE/DGLR/SETP

Fifth Biannual Flight Test Conference. Ontario,

California. May 1990.

. Butts, Stuart, and Alan Lawless. "Flight Testing for Aircraft

Agility." AIAA Paper AIAA-90-1308.

AIAA/SFTE/DGLR/SETP Fifth Biannual Flight Test

Conference. Ontario, California. May 1990.

. Liefer, Randall K., et al. "Assessment of Proposed Fighter

Agility Metrics." AIAA Paper AIAA-90-2807. AIAA

Atmospheric Flight Mechanics Conference. Portland,

Oregon. August 20-22, 1990.

10. Roskam, Jan. Air Diane Flight Dynamics and Automa, ti_ Flight

Controls Part 1. Lawrence, Kansas: Roskam Aviation and

Engineering Corporation, 1982.

91

11.Roskam, Jan. AirDlane Design Part VI; Preliminary Calculatiqn

of Aerodynamic. Thrust and Power Characteristics,.

Lawrence, Kansas: Roskam Aviation and Engineering

Corporation, 1987.

12.McRuer, Duane, and Irving Ashkenas. Aircraft Dynamic and

Automatic Control. Princeton, University Press, 1973.

13.Bitten, R. "Qualitative and Quantitative Comparison of

Government and Industry Agility Metrics." AIAA Paper

AIAA 89-3389. AIAA Atmospheric Flight Mechanics

Conference. Boston, Massachusetts. August 14-16,

1989.

14. Skow, A.M.', et al.

Paper AIAA 85-1779.

Mechanics Conference.

21, 1985.

"Advanced Fighter Agility Metrics." AIAA

AIAA Atmospheric Flight

Snowmass, Colorado. August 18-

15.Yajnik, Kirit S. "Energy-Turn-Rate Characteristics and Turn

Performance of an Aircraft." Journal of Aircraft, Vol.

14, May 1977, 428-433.

92

16. Riley, D., and M. Drajeske. "Status of Agility Research at

McDonnell Aircraft Company and Major Findings and

Conclusions to Date." ICAS Paper ICAS-90-5.9.4. ICAS,

Congress, 17th. Stockholm, Sweden. September 9-14,

1990.

17. Riley, D., and M. Drajeske. "An Experimental Investigation of

Torsional Agility in Air-to-Air Combat." AIAA Paper

AIAA 89-3388. AIAA Atmospheric Flight Mechanics

Conference. Boston, Massachusetts. August 14-16,

1989.

93

APPENDIX A

DESCRIPTION OF BASELINE AIRCRAFT FOR VERIFICATION AND

EXAMPLESTUDIES

This section describes the theoretical model of the Northrop

F-20 Tigershark fighter aircraft used during verification of the

agility module and during the example studies of Chapter 8.

The overall weight, engine thrust and external dimensions of

the Tigershark were matched as best as possible for the available

information. The aerodynamics and component weight breakup were

completely generated internally by ACSYNT. In addition, the engine

performance was obtained from an engine deck obtained from NASA-

Ames and not necessarily the General Electric F-404 used on the

Tigershark. This data should thus not be considered real data from

the Tigershark. This aircraft was simply used as a typical modern

aircraft in the fighter class.

94

The general configuration data for the Tigershark model is:

**** AGILITY TEST MODEL (F-20 WITH 2 AIM-9L'S) DEC92'-JAN93'****

DISTANCES IN FEET WEIGHTS IN LBS. FORCES IN LBS. PRESSURES IN LBS/FT**2

GENERAL FUSELAGE WING HTAIL VTAIL

WGROSS 18201. LENGTH 46.5

W/S 91.0 DIAMETER 3.9

T/W 0.62 VOLUME 426.0

N(Z} ULT 13.5 WETTED AREA 463.8

CREW i. FINENESS RATIO 11.9

PASENGERS 0.

ENGINE WEIGHTS

NUMBER I. W %WG

LENGTH 9.5 STRUCT. 5279. 29.0

DIAM. 2.2 PROPUL. 2323. 12.8

WEIGHT 1023.1 FIX. EQ. 4110. 22.6

TSLS 11234. FUEL 5126. 28.2

SFCSLS 0.75 PAYLOAD 1162. 6.4

AREA 200.0 61.8 39.6

WETTED AREA 292.3 70.9 77.6

SPAN 26.7 15.3 6.4

L.E. SWEEP 32.7 32.2 36.3

C/4 SWEEP 25.0 25.0 25.0

ASPECT RATIO 3.56 3.79 1.04

TAPER RATIO 0.23 0.24 0.28

T/C ROOT 0.05 0.04 0.04

T/C TIP 0.05 0.04 0.04

ROOT CHORD 12.2 6.5 9.6

TIP CHORD 2.8 1.5 2.7

M.A. CHORD 8.5 4.6 6.8

LOC. OF L.E. 21.9 36.6 33.3

The maneuver specifications for the Combat Cycle Time metric

of Chapter 8 were"

ETADE= 1. O,

AMAX=I5.0,

MLEAD=0.05,

$END

MANEUV. MACH ALT.

SEGMENT

NSEG:7, JMAX=500, DT=0.1,

IYY=I4000.0, 300.0, 0.0, 0.0 0.0, 0.0, 0.0,

IXX=I0500.0, 500.0, 0.0, 0.0 0.0, 0.0, 0.0,

LP=-7.0, LDA=75.0,

FBRAKE=5.0 LAMDOT=45.0,

KARB=0, IPRINT=I,

LOAD HEAD BANK AILN WCOMBP A M B T THR THRVECT

FACT CHANGE ANGLE DEFL - + +

............................................................

* METRIC 0.90 15000 0.60 0 0 0 0 1 2

ROLL 0.00 1.0 0.0 81.S 5.0 0 0 0 0

PITCH 0.00 7.0 0.0 0.0 0.0 0 0 0 0

TURN 0.00 7.0 166.5 0.0 0.0 0 0 0 0

PITCH 0.00 1.0 0.0 0.0 0.0 0 0 0 0

ROLL 0.00 1.0 0.0 0.0 -5.0 0 0 0 0

ACCEL 0.90 1.0 0.0 0.0 0.0 0 0 0 0

0. 0.

The user's manual included in this appendix provides

explanation of the above parameters.

95

APPENDIX B

AGILITY MODULE USER'S MANUAL

96

[A. Introduction I

Much of present fighter research has focused on improving

aircraft agility. The problem is that agility is a poorly defined

concept. There have been many new ideas to improve an aircraft's

combat effectiveness and many of these ideas have developed into a

unit of merit or metric. Most agility metrics can be separated into

two categories; transient and functional. The transient metrics deal

with an aircraft's ability to perform quick actions such as rolls,

pitches and nose pointing maneuvers. Functional metrics deal with

longer time scale maneuvers such as transitions from one spatial

location and orientation to another location and orientation, or

transition from one energy level to another. Typically, functional

metrics have transient type maneuvers within them. For both

transient and functional metrics, time is almost always the driving

criterion; the more agile aircraft performs the metric in the least

amount of time.

The architecture of this agility module does not cater to one

specific agility metric but is designed so that a number of metrics

may be analized. This routine can analyze functional metrics and

track the position and energy level of an aircraft through a variety

of trajectories. Functional metrics typically Consist of some

transient segments (rolls and pitches) so they have been includeded

in the module. However, these models are rudimentary and while

satisfactory for functional metric analysis, they are not as

appropriate for discrete transient metrics. Yet, the pieces are there

and as ACSYNT's stability derivative and control system analysis

improves, the transient segment analysis can be improved.

The agility module can only analyze those metrics that lie in an

horizontal plane. The altitude is specified by the user and this

altitude is maintained; there is no diving or climbing.

98

PRKClDINQ PA_E _LAt_K NOT F,_',.Mt_D

lB. Methodolo_ly I

The architecture of the agility module consists of a series of

subroutines that "fly" an aircraft through a level maneuver. The

basic output of the module is the time to complete the maneuver. It

is assumed that maneuvers consist of discrete actions like rolling

to a bank angle, pitching to a load factor, turning to a heading angle

or accelerating to a Mach number. These actions are refered to as

maneuver segments. It is the combined sequence of these segments

that represent the aircraft's maneuver flightpath and performance.

There is a subroutine that performs each of the segment categories

(ROLL, PITCH, TURN, ACCEL). The controlling subroutine (AGILCON)

calls these maneuver segment subroutines in the user specifiedorder.

The maneuver segment subroutines perform their operations in

time steps. Each of the segment subroutines track the following

sixteen state variables through the duration of the segment:

Mach number

Axial acceleration (g's)

Turn rate (deg/sec) Heading angle (degrees)

Bank angle (degrees) X position (feet)Thrust vector angle (degrees)

Drag coefficient

Turn radius (feet)

Gross thrust (pounds) Net thrust (pounds)

Angle of attack (degrees) Load factor (g's)

Roll rate (deg/sec)

Y position (feet)Lift coefficient

The coordinate system of the maneuver arena

The geometry of the maneuver arena is illustrated in figure B.1

The X and Y variables represent the horizontal plane at the given

metric altitude. The aircraft starts at the origin with its nose

pointing in the positive X direction. The heading angle is referenced

to the positive X direction so the aircraft begins with a zero headingangle.

Running agility metrics

There are two methods to run agility metrics.

pick a standard metric like "Combat Cycle Time."

99

The first is to

This metric

automatically calls the maneuver segment routines in the required

order to perform the combat cycle time metric.

The second method is to build up a user-defined metric out of

the individual maneuver segments (ROLL, PITCH, TURN, ACCEL), inany order.

Up to 50 maneuver segments can be implemented in the agility

module. There are no restrictions on the type of these segments.

However, a new metric must begin with a METRIC segment (seedescription of maneuver segment options).

The doghouse plot and corner speed

The general character of the agility module is to operate on the

upper boundary of what is frequently refered to as the doghouse plot.

This is a graph of turn rate versus speed or Mach number (see figure

B.2). The upper boundary of this graph indicates the maximum turn

rate for a given Mach number.

As shown in figure B.2, there is a peak in the upper boundary.

This peak represents the highest turn rate for any Mach number. The

Mach number corresponding to the peak is usually called corner

speed.

The aircraft's turn rate is limited by different constraints

depending on which side of corner speed it is flying. Above corner

speed, the aircraft can aerodynamically generate a higher load

factor than the aircraft's structure can withstand. The aircraft is

said to be load limited with the max turn rate determined by the max

designed load factor. Below corner speed, the aircraft is operating

at its maximum lift coefficient and cannot aerodynamically generate

the design load factor. In this region the aircraft is said to be lift

limited.

From the above discussion, the definition of corner speed can be

inferred; the Mach number that produces the max design load factor

at maximum lift coefficient is the corner speed.

Turning speed (MTURN)

The general logic of the code centers around a certain Mach

number called "turning speed" (MTURN). This speed is used as a100

dividing line between two sets of user input; a throttle and thrust

vector command for above MTURN and a throttle and thrust vectorcommand for below MTURN.

MTURN is specified one of three ways. The first method

designates MTURN as the corner speed calculated for the particularmetric altitude, load factor and max angle of attack. The other two

methods, which will be addressed later, are incorporated to give theuser more control over MTURN for metrics that do not involve turns.

The user may use another variable to adjust the throttle and

thrust vector command schedule. If the variable MLEAD (Mach LEAD)is used, the throttle schedule described above is altered. This

command strategy attempts to better capture MTURN by anticipating

the approach of turning speed (by a factor of MLEAD) and starting thethrottle change earlier (see figure B.3).

Figure B.4 shows the three regions of throttle command created

by the parameters MTURN and MLEAD. The above-corner-speedcommand is used only if the Mach number is above MTURN+MLEAD.

Conversely, the below-corner-speed command is used only if theMach number is below MTURN-MLEAD. If the Mach number lies in the

region between MTURN+MLEAD and MTURN-MLEAD, the throttle

command is the thrust required to sustain the turning load factor atMTURN.

Roll methodology

Aircraft roll maneuvers use a minimum-time control strategy.

The roll begins with a step input aileron deflection. As roll rate

increases and the roll progresses, there is a point in time where a

reversal step input of the aileron would decelerate the roll rate to

zero just as the desired bank angle was captured. This time is

calculated and the time history of the roll then generated. A single

degree of freedom decaying exponential function is used as a time

response model.

Pitch methodology

The pitch routine uses a short period approximation transfer

function for the time response. The control input is a step from the101

starting trimmed control deflection to that required to trim at theending angle of attack.

The internally calculated damping derivatives are adjusted so

that the damping ratio is at least 0.70. Also, the pitching moment

slope is constrained to be -0.1 or less. Therefore, negatively stable

aircraft (positive slope) are constrained to a positively stable

response. These damping ratio and pitch slope constraints are

incorporated to approximate the effects of a flight control system.

Turn methodology

The turn segment flies the aircraft through a level turn. The

specified load factor is maintained as long as the aircraft is not lift

limited. If it is lift limited, the maximum angle of attack is

maintained and the load factor drops off as the aircraft decelerates.

At each time step, the bank angle is calculated to maintain a

level turn. Therefore, as load factor drops off the bank angle willdecrease.

Throttle methodology

The throttle subroutine generates time responses from anystarting thrust level to any ending thrust level. The thrust transient

models used are from a modern ('90) fighter class turbofan engine.The type of transients modelled are idle to dry, idle to wet, wet to

idle, wet to dry, and dry to idle. Throttle changes starting or endingbetween idle and dry or between dry and wet do not have their own

time responses but are interpolated from the five responses statedabove.

Thrust vectoring

The thrust vector is referenced to the aircraft body axis and canbe directed to any angle between the centerline (zero) and the

opposite direction of the centerline (180). Vectoring in the normaldirection would be an angle of 90 degrees. There is a user defined

rate at which the vector angle changes.

The logic is set so that the normal component of thrust and the

lift force add up to the desired load factor. Therefore, for102

equivalent load factors, a vectored thrust turn would be conducted

at a lower angle of attack than a corresponding non-vectored thrustturn.

Y

(feet)

!

X (feet)v

Figure B.1. CoordinateSystem OfThe Maneuver Arena

103

TurnRate

Lift limitedturn

• o

Stall Corner

speed speed Mach Number

Figure B.2. The Doghouse Plot

104

Mach

MTURN

MLEAD>0: ( bold plot ) throttle changes at P1, in

this example, MTURN is better capturedby the early throttle change

MLEAD=0: (thin plot) throttle changes at P2 (MTURN)results in poor capture

.... _.....

h.._

v

Time

Figure B.3. Effect Of MLEAD During Deceleration

To Capture Turning Speed

I I

Thrust equal to drag at iI turning speed and load I

factor is commanded 'Throttle command for below L_ _i Throttle command for abow

turning<speed is commanded I I I turning speed is commande(:_._

IjMLEAD_._,jl MLEAD /

MTURN

Figure

Mach Number

B.4. Throttle Command As A

Function OF Mach Number

105

IC. Agility Metric Options I

1. Combat Cycle Time

The standard combat cycle time metric takes .an aircraft

through a level turn of a specified heading change. The idea is to

turn at high 'g', capture the new heading angle and then accelerate

back to the starting Mach number. The figure of merit for this

metric is the time to complete the entire maneuver. Figure C.1

illustrates the combat cycle time circuit.

(13rr"¢-

Vc Vl

Mach

Legend"

V 1 - starting and ending speedt l - time to bank into turn

t 2 - pitch up to load factort31 -

accelerate back to starting Machlevel turn

t32- time spent in lift limitedlevel turn

Vc- corner speedt4- pitch down to unity load factort5- roll to wings level

time spent in load limited t6-number

time to

106

Figure C.1. Combat Cycle Time Maneuver Circuit

ID. Input File Architecture I

The agility module must be entered in the ACSYNT control block.

The minimum entries are the read and execute rows. The execute

entry should be -12. The negative sign causes agility to be executed

after weight convergence. If agility output is desired in the main

ACSYNT output file, an entry must be placed in the output row of the

module call matrix. If this entry is not made, output will only be

written in agility's output file.

An input block must also be included in the input file; figure D.1

illustrates a sample input block.

1. A_ailitv Namelist ($AGILIN)

...................... Real format ......................

Name Default DescriDtion/_Jn il;s

DT O. 1 Time step increment(seconds)

IYY*7 2OOOO.0 Pitch axis moment of inertia

array. There are seven

elements which correspond to:IYY(1)= clean aircraft, zero

fuel

IYY(2)= added IYY due tointernal fuel

IYY(3)= "external fuel

IYY(4)= "ammunition

IYY(5)= "missiles

IYY(6)= " bombs

107

IXX*7

ETADE

LP

LDA

AMAX

FBRAKE

MLEAD

8000.0

2.5

-7.0

75.0

15.0

3.0

0.04

IYY(7)= "external tanks

If WCOMBP (in agility formattedinput) is >1.0 (ie. it is theactual weight of theaircraft) then only the firstelements are used.

Non-dropable stores, pylons, etc,

should be included in IYY(1).(slug*ft^2)

Lateral axis moment of inertia

array. The description of IYYapplies here also.(slug*ft^2)

Efficiency of the pitch controlsurface. ETADE is 1.0 for an all

moving tail. For an elevator it is

less than one. See appendix forcalculation method.

Roll damping dimensionalderivative

(1/sec)

Aileron effectiveness dimensional

derivative

(1/see)

Angle of attack limit(degrees)

Airbrake equivalent flat platearea(ft^2)

Mach number lead. If acceleratingthrough corner speed, the above-

corner power setting will be

engaged at MLEAD below corner

speed. If decelerating throughcorner speed, the below-corner-

speed power setting will be

108

engaged at MLEAD above cornerspeed. If the Mach number isbetween MTURN+MLEAD andMTURN-MLEAD the throttlecommand will be thrust equal tothe drag at the turning condition(MTURN and the turning loadfactor).• This variable can have

pronounced effects on the captureof turning speed and the entiremetric in general.

.................... IntegerName Df___e.J_a...u_t

KARB 0

NSEG 1

IPRINT 0

JMAX 500

format ...........................

Description

Airbrake toggle variable:0= Do not use airbrake1= Use airbrake

Note: if the airbrake is used, then

an internal variable controls

when it is and when it is not

used. This variable deploysthe airbrake while above

turning speed and retracts it

below turning speed.

Number of maneuver segments informatted input block

(50 maximum)

Output print controller:

0= Print summary output only

1= Print standard output

2= Print detailed output

(see section E)

Maximum number of time stepsallowed per metric. If the time

step (DT) is 0.1, the default value

(500) would allow for fifty109

seconds of maneuver time. Themaximum number is 750. If moreare required the variable arraysmust be increased in the /TRACK/

and/POWER/common blocks as

well as the dimension of TIME() inthe AGILE subroutine.

2. Formatted Input

The formatted input block is where the maneuver sequence is

specified. A series of segments such as ROLL, PITCH and TURN are

implemented to build the desired metric. In addition, there are

certain segment types that perform an entire standard agility

metric. In either case the beginning of a new metric is designated

by the input of a "METRIC" segment.

The maneuver segment options are:

METRIC: This segment tells the code to start a new metric.

Inputs are the starting flight conditions.

ROLL: Here the aircraft is rolled to a specified bank angle. Theload factor entered under this row is the starting loadfactor. The ROLL subroutine maintains this load factor

for the duration of the roll. For convenience, table D.II

lists the proper level turn bank angles for common loadfactors.

PITCH:

TURN:

The pitch segment rotates the aircraft to a desired load

factor. The starting bank angle is maintained for the

duration of the pitch.

WARNING: for aircraft that are statically unstable, the

pitch routine fudges the pitching moment slope to be

slightly negative to prevent the response equation fromblowing up.

This segment turns the aircraft to a specified headingangle. The heading angle input in this column is not the

110

TURN: This segment turns the aircraft to a specified headingangle. The heading angle input in this column is not thenumber of degrees to turn through but the actual desiredheading angle. The aircraft is always assumed to start ametric with a zero heading angle. The subroutine triesto maintain the specified load factor but if the aircraftdecelerates to the lift limited region the maximumangle of attack will be held and the load factor will thusdecay.

ACCEL: The accel segment accelerates or decelerates the

aircraft to a specified Mach number. This segmentbegins with and maintains a wings level l g horizontalflight path.

CCT: This segment "flies" the aircraft through an entire

combat cycle time metric (see figure C.1).

The formatted input is organized into sixteen columns, these are:

MANEUV. SEGMENT

MACH

ALTITUDE

LOAD FACT

HEAD ANGLE

BANK ANGLE

AILN DEFL

This list contains the type of maneuver

segments (see segment description)

Mach number, represents:

starting Mach in METRIC segments

turning Mach in TURN or CCT segmentsending Mach in ACCEL segments

Metric altitude in feet, used only in

METRIC segment

Load factor, used by all but METRIC andACCEL segments

Ending heading angle, used by TURN andCCT segments

Ending bank angle in degrees, used only byROLL segments

Aileron deflection in degrees, used by ROLLand CCT segments

111

W_BP Specifies aircraft weight, used only byMETRIC segments

<1.0 fuel fraction (total usable fuel)>1.0 - actual aircraft weight in pounds

A,M,B,T

THR

Drop flags for ammunition, missiles,bombs, and external fuel tanksrespectively. Used by every segment butonly if WCOMBP in the METRIC segment isless than 1.0. The drop flags recomputeweight, moment of inertias and drag at theend of each segment.

0 - include store weight and drag

1 subtract store weight and drag forthe remainder of the metric

'+': Throttle command for operation above

turning speed

'-" Throttle command for operation below

turning speedThrottle commands are:

1: maximum power (full A/B)

2: maximum dry power

3: maintain starting trimmed flight

power4: thrust = drag (@turning speed and

load factor)5: flight idle

Throttle commands may be entered under

any or all segments but they are required

under the METRIC segments. If they are

only entered in the METRIC segments thenthese throttle commands are used for the

entire metric.

THRVECT '+': Thrust vector angle command for

operation above turning speed

'-" Thrust vector angle command for

operation below turning speed

Zero degrees refers to thrust along

axial direction while ninety degreesrefers to thrust normal to body axis.

Notes: The turning speed (MTURN) is calculated one of three ways:112

1" If there are no TURN or CCT segments in the input file thenMTURN is designated as the starting Mach number.

2: If there are TURN or CCT segments, then MTURN is thecorner speed for the given metric altitude, turning loadfactor and maximum angle of attack.

3: However, if the Mach entry under the TURN or CCT segmentis nonzero, the corner speed designation (2) is overwrittenwith this Mach entry.

If there are or more TURN segments within one metric, theturning speed will be set by the information in the last TURNsegment.

It is up to the user to ensure that the tracked variables arecontinuous from one segment to the next.Some examples are-

The load factor for a roll should be equivalent to the endingload factor of the previous segment.If a turn is desired following a roll, a pitch segment isrequired to transition from the rolling load factor to thedesired turning load factor.

The starting Mach number of an acceleration segment shouldbe the ending Mach number of the previous segment.

Table D.I summarizes the /__ inputs for different segmenttypes.

Table D.I Required Inputs For Maneuver Segments

MANEUV. MACH ALT. LOAD HEAD 8AHK AILN WCOMBP A M B T THR THRVECTSEGMENT FACT CHANGE ANGLE DEFL

........... - + - ÷

.................................................

" METRIC X X

X X X X X X X X X

ROLL ]': Y. X X X :< X

PITCH ,_[ X X X X

TURN ],L ]'[ i'l X k v XACCEL X ""

X X X X

CCT .< X "< X X ]4 X X X X X X

113

*** AGILITY ***

NSEG:7, JMA;<= 500, DT:0. i,

IYY=I4000.0, 300.0, 0.0, 0.0, 0.0, 0.0, 0.0,

IXX=I0500.0, 500.0, 0.0, C'.C:, 0.0, 0.0, 0.0,

ETADE= 1 .{?, LP=-7. C:, LDA=_ 5.0,

AbfiAX= 15.0, FBRAKE:5.0, L_.MDOT= 45.0,

MLEAD=0.05, KARB:0, IPRINT=!,S END

MANEUV. MACH ALT. LOAD HEAD EAN_: AILN WCOMBP A M E T THR THRVECT

SEGMENT FACT CHANGE ANGLE DEFL -

..................................................... - _ _:__

* METRIC 0.90 15000 0.60 I 0 I I ] 2

ROLL 0.00 1.0 0.0 83.6 5.0 0 0 0 0

PITCH 0.00 9.0 0.0 0.0 0.0 0 0 0 0

TURN 0.00 9.0 169.3 0.0 0.0 0 0 0 0

PITCH 0.00 1.0 0.0 0.0 0.0 0 0 0 0

ROLL 0.00 1.0 0.0 0.0 -5.0 0 0 0 0

ACCEL 0.90 ].0 0.0 0.0 0.0 0 0 0 0

0. 0.

Figure D.1. Sample Input File

Notes on figure D.I:

As in other ACSYNT namelists, $AGILIN is indented onespace.

After the namelist, three lines are read before the

formatted input is read. These three lines are for the

format column header. Any fewer or any more lines willmess up the input.

The formatted input statement is:

FOR M AT(2X,A6, F6.2, F8.0, F5.1, F7.1, F6.1, F5.1,

F10.2,12,12,12,12,1X,12,12,1X,F5.0,F5.0)

114

Table D.II Bank Angles Required To Coordinate Level Turns

Load Factor .Bank Angle Load Factor

1.0 00.0 5.5 79.5

1.5 48.2 6.0 80.4

2.0 60.0 6.5 81.2

2.5 66.4 7.0 81.8

3.0 70.5 7.5 82.3

3.5 73.4 8.0 82.8

4.0 75.5 8.5 83.2

4.5 77.2 9.0 83.6

5.0 78.5 9.5 84.0

Equation: bank angle= cos-l(1/Ioad factor)

Example: Suppose a 4.5 g turn was desired. According to the above

table, a roll to a bank angle of 77.2 degrees should be

performed first. After the roll a pitch to 4.5 g's wouldthen hold the aircraft in a level turn.

I E Output File Architecture

The agility module has three levels of output, these are:

Summary- only the total time to complete eachmetric

Standard-summary output plus the time per segmentbreakdown and some other key parameters(see output example below)

Detailed- standard output plus complete time trackof state variables.

115

The output is contained in three files, these are:

fort.30- contains the summary and standard output andthe entire time tracks of the following:

Mach numberAxial accelerationLoad factorRoll rateX position

Net thrustangle of attackTurn rateBank angleY position

Segment type indicator

fort.31 - contains the entire time tracks of the following:Gross thrust Percent core thrustPercent A/B thrust Lift coefficientDrag coefficient Turn radius

ACSYNT- The user can choose any of the three outputlevels for the ACSYNT output file. The selectedoutput level holds for all metrics. This is done byspecifying the output control variable IPRINT in thenamelist.

IPRINT=0: Summary

1: Standard

3: Detailed

IF. COPES Interface I

COPES has access to 25 variables in the agility module. The

first five elements in this array are reserved for the total times

required to complete the first five metrics. Elements 6 through 25

are open to the user. However, use of these elements requires

modification of the code. The user must alter the subroutines to

extract the desired parameter and then assign it an element location

in the COPES array.

116

dix

Construction of the pitch control surface effectiveness

(ETADE)

The method used to calculate the pitch control surface

effectiveness is straight out of Jan Roskam's Aiplane Design Series

Part 6. The equation below corresponds to equation 10.94 on page437 of Roskam's text. In this equation, the parameter O_Seis

equivalent to ETADE used below. The attached figures were copiedfrom this text and are included here for convenience.

ETADE= Kb*[cl(_/(clS)theory](ClS)theory*(k'/clo_h)[((z(_)C L/((z(5)cl)]

where:

Kb is the elevator span factor obtained from Figures8.51 and 8.52. Note: in Figure 8.52, the abscissa _1should be considered as the z_l of Figure 8.51.

[cls/(clS)theory] is found from Figure 8.15.

(clS)theory is found from Figure 8.14.

k' is found from Figure 8.13.

[((z(5)CL/(o_(_)cl)]is found from Figure 8.53.

117

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FLAP DEFLECTION, 6:[(d¢1;)

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118

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119

Figure 8.$_ Procedure for EBtimatin o Kb

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Fiaure 8. S2 Effect of Taper Ratio and Flae Span on Kb

Part VI Chapter II Page g6o

120

co P'lE,,_ i= li Dr,,.i : IIRF. I.

121